Education Commons^™

Using Visual Imagery To Develop Multiplication Fact Strategies, Gina Kling

Dissertations

The learning of basic facts, or the sums and products of numbers 0–10 and their related differences and quotients, has always been a high priority for elementary school teachers. While memorization of basic facts has been a hallmark of elementary school, current recommendations focus on a more nuanced development of fluency with these facts. Fluency is characterized by the ability to demonstrate flexibility, accuracy, efficiency, and appropriate strategy use. Despite recommendations to focus on strategy use, there is insufficient information on instructional approaches that are effective for developing strategies, particularly for multiplication facts. Using visual imagery with dot patterns has …

Characterizing Undergraduate Students’ Proving Processes Around “Stuck Points”, Yaomingxin Lu

Dissertations

Learning to prove mathematical propositions is a cornerstone of mathematics as a discipline (de Villiers, 1990). However, since proving is a different mathematical activity as compared to students’ prior experience, research has also shown that many undergraduate students struggle to learn to prove, including those who major in mathematics (Moore, 1994; Selden, 2012). While the field has generated research that has analyzed the final products of proof (Selden & Selden, 2009) and there are frameworks for analyzing problem-solving processes (e.g., Carlson & Bloom, 2005; Schoenfeld, 1985, 2010), much remains to be known about analyzing undergraduate students’ proving processes. With a …

Ready To Engage? Urban Middle School Teachers’ Responsiveness To Targeted Engagement Interventions On Their Virtual Instructional Practices: An Action Research Study, Svetlana Nikic

Dissertations

Teachers’ effectiveness is associated with their instructional practices and is ultimately linked to students’ learning outcomes. In order to impact teachers’ effectiveness, schools focus substantial effort and resources on professional development led by an assumption that teachers’ classroom practices can be improved through targeted interventions. Even if this premise is correct, little information is available about how much a teacher’s practice may change through interventions, or which aspects of instructional practice are more receptive to improving teacher effectiveness (Garret et al., 2019).

This study took place at an urban middle school and examined teachers’ responsiveness to targeted engagement intervention in …

Saudi Elementary Mathematics Teachers’ Knowledge For Teaching Fractions, Mona Khalifah A Aladil

Dissertations

Recent reform efforts in Saudi Arabia attend to mathematics instruction with a great deal of emphasis to improve Saudi mathematics education. Studies in different countries have confirmed that teachers’ mathematical knowledge for teaching plays an important role in mathematical quality of instruction and students’ achievement (e.g., Ball, 1990; Baumert et al., 2010; Hill, Rowan, & Ball, 2005). Yet few studies about mathematics teachers’ knowledge for teaching have been conducted in the Saudi context. This study investigates Saudi elementary mathematics teachers’ knowledge for teaching in the content strand of rational numbers with an emphasis on fractions, which is an important step …

The Role Of Sampling Variability In Developing K-8 Preservice Teachers’ Informal Inferential Reasoning, Omar Abu-Ghalyoun

Dissertations

Recent influential policy reports, such as the Common Core State Standards (CCSS-M, 2010) and Guidelines for Assessment and Instruction in Statistics Education Report, (GAISE, 2007), have called for dramatic changes in the statistics content included in the K-8 curriculum. In particular, students in these grades are now expected to develop Informal Inferential Reasoning (IIR) as a way of preparing them for formal concepts of inferential statistics such as confidence intervals and testing hypotheses. Ben-Zvi, Gil, & Apel, (2007) describe IIR as the cognitive activities involved in informally making statistical inferences. Over this path from informal to formal inference, many important …

The Bellringer Sequence: Investigating What And How Preservice Mathematics Teachers Learn Through Pedagogies Of Enactment, Mary A. Ochieng

Dissertations

This study examines preservice teacher learning through pedagogies of enactment—approaches to teacher education that allow preservice teachers to learn by doing what teachers do. Preservice teacher (PST) learning is examined through the implementation of the Bellringer Sequence (BRS), a pedagogy of enactment conceptualized in the study. The BRS is centered around bellringers—brief mathematical tasks implemented as students arrive for class. The BRS is a sequence of four activities centered on a bellringer: preparation (for teaching a bellringer) implementation (of the bellringer with peers), debriefing (discussing the implementation as colleagues), and written reflection (about the effectiveness of the bellringer).

Practice-based approaches …

Pedagogical Moves As Characteristics Of One Instructor’S Instrumental Orchestrations With Tinkerplots And The Ti-73 Explorer: A Case Study, James L. Kratky

Dissertations

Those supporting contemporary reform efforts for mathematics education in the United States have called for increased use of technologies to support student-centered learning of mathematical concepts and skills. There is a need for more research and professional development to support teachers in transitioning their instruction to better meet the goals of such reform efforts.

Instrumental approaches to conceptualizing technology use in mathematics education, arising out of the theoretical and empirical work in France and other European nations, show promise for use to frame studies on school mathematics in the United States. Instrumental genesis is used to describe the bidirectional and …

The Effects Of Standards-Based Grading On Student Performance In Algebra 2, Rachel Beth Rosales

Dissertations

The use of standards-based grading in American public schools is increasing, offering students, parents, and teachers a new way of measuring and communicating about student achievement and performance. Parents indicate an appreciation for this method of grading, and students at the elementary grades (K-6) have improved standardized test scores in reading and math as a result of its implementation. This study seeks to determine whether standards-based grading has the same effect on students at the high school level (grades 9-12) by comparing end-of-course test scores and posttest scores of Algebra 2 students enrolled in a standards-based graded classroom with to …

Characterizing And Supporting Change In Algebra Students' Representational Fluency In A Cas/Paper-And-Pencil Environment, Nicole L. Fonger

Dissertations

Representational fluency (RF) includes an ability to interpret, create, move within and among, and connect tool-based representations of mathematical objects. Taken as an indicator of conceptual understanding, there is a need to better support school algebra students’ RF in learning environments that utilize both computer algebra systems (CAS) and paper-and-pencil. The purpose of this research was to: (a) characterize change in ninth-grade algebra students’ RF in solving problems involving linear equations, and (b) determine conditions of a CAS and paper-and-pencil learning environment in which those students changed their RF.

Change in RF was measured by comparing results from initial to …

Assessing The Impact Of A Computer-Based College Algebra Course, Ningjun Ye

Dissertations

USM piloted the Math Zone in Spring 2007, a computer-based program in teaching MAT 101and MAT 099 in order to improve student performance. This research determined the effect of the re-design of MAT 101 on student achievements in comparison to a traditional approach to the same course. Meanwhile, the study investigated possible effects of the Math Zone program on students’ attitude toward studying mathematics.

This study shows that there was no statistically significant difference on MAT101 final exam scores between the Math Zone students and the Classroom students in Fall 2007, Spring 2008 and Fall 2008. At the same time, …

Mastery Of Sixth-Grade Mathematics Expectations As Measured By The Seventh-Grade Michigan Education Assessment Program From 2005 To 2007, Marian Prince

Dissertations

Purpose

The purpose of this study is to document sixth-grade mathematics mastery as measured by the seventh-grade Michigan Education Assessment Program (MEAP) over a period of 3 years: 2005, 2006, and 2007. This study investigated whether mathematics performance in Michigan is related to ethnicity by analyzing student responses on the seventh-grade MEAP which evaluates students’ mastery of the Michigan sixth-grade mathematics expectations.

Method

Data from the Michigan Department of Education (MDE) containing the student scores of individual test items on the mathematics Michigan Education Assessment Program (MEAP) for seventh-grade students in Michigan for 2005 to 2007 formed the basis for …

Empirical Development Of An Instructional Product And Its Impact On Mastery Of Geometry Concepts, Donaldson Williams

Dissertations

Problem

Relatively poor levels of mathematical thinking among American school children have been identified as a major issue over the past half century. Many efforts have been made to increase the mathematics performance of children in schools. Additionally, out-of-school-time programs have attempted to address this issue as well. Holistic development is one of the distinguishing features of Seventh-day Adventist instructional programs. Yet, as of 2007, the Pathfinder program, an informal educational program operated by the world-wide Seventh-day Adventist church, had no instructional product designed to foster participants’ cognitive development in mathematics. This study focused on the empirical development of an …

What Allows Teachers To Extend Student Thinking During Whole-Group Discussions, Nesrin Cengiz

Dissertations

Research indicates that extending students' mathematical thinking during whole-group discussions is challenging, even for the most experienced teachers. That is, it is challenging for teachers to help students move beyond their initial mathematical observations and solutions during whole-group discussions. To better understand this phenomena, the teaching of six experienced elementary school teachers, who had been teaching aStandards-based curriculum for several years and had participated in a multi-year professional development project focused on that curriculum, is explored in this study. In particular, two issues are addressed: what it looks like to extend student thinking during whole-group discussions and how …

An Investigation Of Secondary Teachers’ Knowledge Of Rate Of Change In The Context Of Teaching A Standards-Based Curriculum, Jihwa Noh

Dissertations

This study investigated teachers' mathematical content knowledge and pedagogical content knowledge with respect to rate of change in the context of teaching a Standards-based high school mathematics curriculum that emphasizes rate of change as a central theme, the Core-Plus Mathematics Project (CPMP) materials. A framework was designed to provide a comprehensive guide for analyzing different aspects of rate of change knowledge incorporating existing frameworks relative to rate of change, NCTM recommendations described in Curriculum and Evaluation Standards for School Mathematics andPrinciples and Standards for School Mathematics (NCTM, 2000), and research related to pedagogical understanding of rate of change.

Data …

How Secondary School Mathematics Teachers Construct An Understanding Of "Appropriate Use" Of Graphing Calculators In The Context Of Collegial Inquiry, Marcia L. Weller Weinhold

Dissertations

No abstract provided.

Variables Related To The Successful Completion Of The First Course In Business Calculus At Three Jamaican Universities, Martin Nkhrama Richards

Dissertations

Problem. Many students at all levels of the education system in Jamaica perform poorly at mathematics. In particular, the results of both the Caribbean Examinations Council and Business Calculus 1 at the university level have reflected a declining trend in mathematics performance in recent years. Consequently, this study sought to investigate the variables related to the successful completion of the first course in business calculus at Jamaican universities. To this end, the study looked at perceptions of students and their professors regarding students' cognitive, affective, and professor effectiveness variables impacting success.

Method. The sample for this study consisted of 389 …