Digital Commons Network^™

Impacts Of Discourse On Algebra Achievement, Higher-Order Thinking, And Student Efficacy At The Secondary Level, Paige Roth

Masters of Arts in Education Action Research Papers

This study explores the impacts of small-group discourse on an eighth-grade algebra course. Participants of the study are 31 eighth grade students in an urban charter school. Data was collected using pre- and post-assessments, observational tracking, classroom discourse rubric, and student journaling. Data was collected over eight weeks. Results showed growth in assessment scores using pre- and post-assessments. There was an increase in class participation, observed through anecdotal notes. Also, using a discourse rubric, student groups increased their scores on questioning and evaluating mathematical concepts. Discourse will continue to be used to improve mathematical understanding and student efficacy. Weekly discourse …

The Effectiveness Of Socratic Teaching As An Intervention In The Instruction Of High School Geometry For Students With Emotional Behavioral Disorders, Adam Wohl

Culminating Projects in Special Education

High school students across the United States continue to struggle to attain mathematical proficiency, let alone achieve deep levels of conceptual knowledge in its various fields. This is particularly true for students with special needs. In this study, the effectiveness of the Socratic method was analyzed using a study on 13 students taking geometry with emotional-behavioral disorders (EBD), autism spectrum disorders (ASD), or other health disorders (OHD), including students with comorbidities between these. Six students were in the experimental group and received the Socratic method as an instructional method for a unit lasting approximately six weeks. Seven students were in …

Meeting Their Needs: The Algebraic Knowledge And Instructional Preferences Of Students With Learning Disabilities, Kayla Neill

Theses and Dissertations

Students with a learning disability (LD) are experts in their lived experiences within the classroom. Yet, little is known about the ways in which students with LD perceive their instruction in mathematics and whether this instruction meets their learning needs. Similarly, the mathematical thinking and content knowledge of students with LD is often excluded from the literature, particularly concerning algebraic concepts. Six high school students with LD from a large urban school district in the northeast United States participated in this two-part study. Semi-structured interviews were used to explore participants’ perceptions about their instruction within Integrated Co-Taught (ICT) mathematics classes. …

The Effects That A Flipped Classroom Has On Engagement And Academic Performance For High School Mathematics Students, Jordan Geraets

Dissertations, Theses, and Projects

Flipped classrooms continue to spark educator’s attention and curiosity as an alternative to the traditional teaching and engagement in a classroom, especially during the time of a global pandemic. New, innovative technology has allowed for educators to be able to evolve their classrooms into new learning environments. Research into how flipped classrooms can impact mathematics classrooms and how students engage and perform differently than in a traditional mathematics classroom was expanded on in this study to determine what benefits there could be for students and how effective the teaching model can be in a class where students often struggle. As …

El Dilema En Los Números: An Examination Of The Historical Exclusionary Mathematics Placement Practices That Prevent Hispanic Level 1 And 2 El Student Participation In Higher-Level Mathematics Courses., Rardy Leandro Pena

Counseling and Psychology Dissertations

The current placement of Hispanic level 1 and 2 English Learner students into mathematics courses has been constructed and propagated by the assumptions that these students enter school in the United States at a lower level in mathematics. This assumption, which has neither been tested nor confirmed, perpetuates the systemic injustices in public education by erroneously creating a homogeneous placement process for Hispanic English Learner students and contributes to the economic, social, and political marginalization often experienced by Hispanic immigrants. The purpose of the current project was to examine the veracity of these assumptions by exploring the mathematics placement practices …

Recruiting Minoritized Mathematics Preservice Teachers With Retention In Mind, Nicholas Scott Kim

Doctoral Dissertations

The primary purpose of this research is to provide insight into the narratives and experiences of minoritized preservice teachers (PST) interested in teaching mathematics and how those experiences impact recruitment and retention of those minoritized teachers. “Minoritized,” as used here, is defined as one who identifies as a person from a historically underserved community based on race or ethnicity. As a result, this study is positioned to provide researchers, educators, and administrators with much needed direction into how to diversify the teaching force beyond the dominant storyline of the White majority, and why it is important to do so.

Narrative …

Middle School Students' Reported Self-Regulation Strategies In Completing Online Mathematics Homework, Pepper Erlinger

Boise State University Theses and Dissertations

The purpose of this qualitative descriptive case study is to benefit our understanding of the potential of online homework as it relates to developing and supporting students’ self-regulated learning (SRL). This descriptive case study explores the use of self-regulated learning (SRL) strategies reported by students in the context of completing online mathematics homework (OHW). Eighth-grade students (10 total) from a traditional middle school were interviewed using a validated data collection instrument, the Self-Regulated Learning Interview Schedule or SRLIS (Zimmerman & Martinez-Pons, 1986, 1988). Students’ open-ended responses were interpreted using a framework of self-regulation theory and coded using 14 self-regulation strategies …

Preschool Children's Development In Number, Geometry, And Executive Function: A Cross-Lagged Examination, Brionne G. Neilson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Children develop rapidly during early childhood, and this includes their mathematics and executive function (EF) skills. Past research has focused on connections between early mathematics and EF, but more work was needed to fully understand these relations. In particular, past studies have generally used numeracy-based measures to assess early mathematics, although professional guidelines indicate a more comprehensive construct that includes geometry. The research herein addresses some of the gaps of previous work as it examines unique connections between early number, geometry, and EF. One hundred eighteen preschool children from urban and rural communities, being an average age of 53 months …

Incorporating Real World Geometry Problems Into Geometry Classrooms, Heather Renee Postier

Undergraduate Honors Thesis Collection

The question posed to conduct this research was:

How do teachers incorporate real world problems into geometry classrooms?

There is no single answer to this question, but there are many answers. The research done in this literature review not only answers this question but also the question of why. The research reviewed was organized into the sections of Inquiry, Student Engagement, and Mathematical Understanding. Teachers can incorporate the real world into mathematics classrooms through inquiry, problem-based learning, and every day real world objects. Teachers should do this because it increases student engagement and leads students to higher mathematical understandings. Not …

The Relationship Between I-Ready Intervention And Grade 8 Mathematical Achievement, Kenyatta Shanta Aldridge

Theses and Dissertations

A problem exists in using educational software as an intervention for middle grades mathematics. The rural middle school used an educational program to improve mathematical achievement; however, the effectiveness of this program was not evaluated. The e-learning theory served as the theoretical framework for this study. The purpose of this explanatory, sequential mixed methods design was to examine the relationship between the i-Ready intervention program and students’ mathematical achievement and to explore teachers’ perceptions of implementing the i-Ready intervention program. The participants included 48 Grade 8 students from one middle school. A series of bivariate correlations was conducted using the …

An Investigation Of The Effects Of Self-Efficacy On Stem Implementation, Caroline Buechel

Curriculum and Instruction Undergraduate Honors Theses

In order to equip students with the 21^st Century skills necessary for today’s society, STEM education must be properly implemented in school curricula (Lamb, Akmal, & Petrie, 2015). To do so, it is important for teachers to possess both proficient knowledge of the subject matter and confidence towards the implementation of STEM. A person’s beliefs about their ability is known as their self-efficacy (Bandura 1997). Related to education, Bandura notes that this self-efficacy affects a teacher’s views on their ability to handle tasks, obligations, and challenges related to a challenge (1997). Additionally, numerous studies indicate that this self-efficacy in …

Mapping Middle School Mathematics Teachers' Curriculum Assemblages: A Post-Qualitative Inquiry, Hilary Rene Tanck

All Dissertations

In my post-qualitative inquiry, I investigated four middle school mathematics teachers’ curriculum work during the COVID-19 pandemic. Curriculum has been undergoing a transformation as teachers have greater access to online resources and digital tools (Pepin et al., 2017; Webel et al., 2015). The transformation was further exacerbated by the changes forced by COVID-19 as teachers scrambled to reimagine their curriculum systems in a different context—virtual, hybrid, and concurrent. This study used a post-qualitative approach branching away from traditional linear notions of curriculum to one that is complex, dynamic, and creative. The goal was to create a space to consider curriculum …

An Exploratory Analysis Of The Bgsu Learning Commons Student Usage Data, Emily Eskuri

Honors Projects

The purpose of this study was to explore past student usage data in individualized tutoring sessions from the Learning Commons from two academic years. The Bowling Green State University (BGSU) Learning Commons is a learning assistance center that offers various services, such as individualized tutoring, math assistance, writing assistance, study hours, and academic coaching. There have been limited research studies into how big data and analytics can have an impact in higher education, especially research utilizing predictive analytics.

This project applied analytics to individualized tutoring data in the Learning Commons to create a better understanding of why those trends happen …

At The Top Of The Chart: A Composite Counterstory Of Black Students’ Mathematical Success, Joslyn N. Richardson

Dissertations

Mathematics as a discipline has ignored the experiences of African American students, making it difficult for them to develop strong mathematical identities and racial identities in relation to math. Black children and their academic achievements are often framed negatively, and underachievement and failure are often emphasized over their brilliance and resilience. This qualitative study adds to the limited body of knowledge by examining student perspectives and socialization factors that contribute to positive math identity and achievement in middle school students. Using a Critical Race Theory framework, data was collected through semi-structured interviews and math autobiographies that were structured around the …

On Tests Of Independence Among Multiplerandom Vectors Of Arbitrary Dimensions., Angshuman Roy Dr.

Doctoral Theses

Measures of dependence among several random vectors and associated tests of independence play a major role in different statistical applications. Blind source separation or independent component analysis (see, e.g., Hyv¨arinen et al., 2001; Shen et al., 2009), feature selection and feature extraction (see, e.g., Li et al., 2012), detection of serial correlation in time series (see, e.g., Ghoudi et al., 2001) and finding the causal relationships among the variables (see, e.g., Chakraborty and Zhang, 2019) are some examples of their wide-spread applications. Tests of independence has vast applications in other areas of sciences as well. For instance, to characterize the …

Matrix Product Structure Of A Permuted Quasi Cyclic Code And Its Dual, Perian Perdhiku

Dissertations

In my Dissertation I will work mostly with Permuted Quasi Cyclic Codes. They are a generalization of Cyclic Codes, one of the most important families of Linear Codes in Coding Theory. Linear Codes are very useful in error detection and correction. Error Detection and Correction is a technique that first detects the corrupted data sent from some transmitter over unreliable communication channels and then corrects the errors and reconstructs the original data. Unlike linear codes, cyclic codes are used to correct errors where the pattern is not clear and the error occurs in a short segment of …

Mindfulness & Mindset: The Winning Combination? The Exploration Of The Unstuck Method® On Developmental Math Students: A Mixed Methods Study, Edite Birnbaum, Edith L. Birnbaum

Graduate Theses & Dissertations

Many students enter colleges having to take non-credit-bearing courses, and many do not pass these courses due to numerous factors, including anxiety and stress, especially in mathematics. Current literature shows how mindfulness-based interventions (Bamber, & Schneider, 2016; Dvořáková et al., 2017; Hidman, 2013; Miller et al. 2019; Regehr et al., 2013) and a growth mindset (Blackwell et al., 2007; Boaler et al., 2018; May, 2009) have a positive effect on student stress, anxiety, and academic success. This mixed-method study focused on the unSTUCK strategy’s impact, a mindfulness-inspired tool, on foundation math students. The unSTUCK strategy is a mindfulness-inspired program. The …

The Relationship Between The Use Of Curriculum Materials And Inquiry-Based Pedagogy, Laura Jo Elzinga

Theses and Dissertations

Little change has resulted from decades of attempts at reforming the teaching of mathematics (Davis et al., 1990). This study involved approximately 43 teachers who had completed an inquiry-based professional development program prior to being provided with a new mathematics curriculum designed to support inquiry-based teaching. It analyzed the relationships between their implementation of the inquiry-based teaching and their use of the curriculum materials. A series of bivariate correlations were run to investigate the relationships between the professional development and aspects related to the implementation of the new curriculum. The factors being so inter-related, it was hypothesized that relationships would …

Metacognition In A Mathematics Classroom, Paige Murta

Honors Projects

The purpose of this action research study is to explore the connections between students’ ability to engage in metacognitive methods, their understanding of mathematical content, and their mathematical performance. By having a group of students engage in a lesson about metacognition and a mathematical modeling problem then comparing their test scores to that of a control group a correlation can be found to analyze the effects of metacognition methods in a mathematics classroom.

Toxic Math-Masculinity: Changing Harmful Lay Theories Of Mathematics To Improve Student Achievement, Zac Kamm

School of Education and Leadership Student Capstone Projects

Students often come into the secondary math classroom with an implicit understanding of mathematics that negatively affects their performance in the classroom. These lay theories often reinforce an entity theory of mathematical ability that views ability as fixed and unchangeable. In turn, this view of mathematical ability influences students’ goal orientations. Research shows the positive benefits of an incremental theory of mathematical ability and a mastery goal orientation on mathematics student achievement. Much of the research literature focuses on describing or quantifying the connection between incremental theories of mathematical ability and student achievement rather than describing effective strategies for changing …

Well-Distributed Sequences: Number Theory, Optimal Transport, And Potential Theory, Louis Max Brown

Yale Graduate School of Arts and Sciences Dissertations

The purpose of this dissertation will be to examine various ways of measuring how uniformly distributed a sequence of points on compact manifolds and finite combinatorial graphs can be, providing bounds and novel explicit algorithms to pick extremely uniform points, as well as connecting disparate branches of mathematics such as Number Theory and Optimal Transport. Chapter 1 sets the stage by introducing some of the fundamental ideas and results that will be used consistently throughout the thesis: we develop and establish Weyl's Theorem, the definition of discrepancy, LeVeque's Inequality, the Erdős-Turán Inequality, Koksma-Hlawka Inequality, and Schmidt's Theorem about Irregularities of …

Construction Of The Universal Second Motivic Chern Class Using Cluster Varieties, Oleksii Kislinskyi

Yale Graduate School of Arts and Sciences Dissertations

Denote by $B\Gamma$ the classifying space of an algebraic group $\Gamma(\mathbb{C})$. In this thesis we will take Milnor's realization of it -- the classifying simplicial space $B_{\Gamma\bullet}$. Consider the weight two motivic complex $ \mathbb{Z}_{\mathcal{M}}(2)$ for a regular algebraic variety $X$, placed in degrees $[1,4]$: $$ B_2(\mathbb{C}(X)) \to \bigwedge^2 \mathbb{C}(X)^* \to \bigoplus\limits_{D\in div(X)}\mathbb{C}(D)^* \to \bigoplus\limits_{D\in cod_2( X)}\mathbb{Z}.$$ Let $G$ be a split semisimple simply connected algebraic group over $\mathbb{Q}$. Then the degree 4 cohomology $H^4(B_{G\bullet}, \mathbb{Z}_{\mathcal{M}}(2))$ is known to be isomorphic to $\mathbb{Z}$. This can be deduced, for example, from the main result of Brylinski and Deligne \cite{BD}, although they …

Dynamics Of Unipotent Subgroups On Infinite Volume Space, Minju Lee

Yale Graduate School of Arts and Sciences Dissertations

This thesis consists of five separate projects. They are organized into the following sections: 1. Orbit closures of unipotent flows for hyperbolic manifolds with Fuchsian ends. In joint work with Oh, we establish an analogue of Ratner's orbit closure theorem for any connected closed subgroup generated by unipotent elements in $\mathrm{SO}(d, 1)$ acting on the space $\Gamma\backslash\mathrm{SO}(d, 1)$, assuming that the associated hyperbolic manifold $M=\Gamma\backslash\mathbb H^d$ is a convex cocompact manifold with Fuchsian ends. 2. Topological proof of Benoist-Quint. Let $G=\mathrm{SO}^\circ(d,1)$, $\Delta

Three Families Of Lie Algebras Of Exponential Growth From Vertex Operator Algebras, Gabriel Legros

Yale Graduate School of Arts and Sciences Dissertations

We study three families of infinite-dimensional Lie algebras defined from Vertex Operator Algebras and their properties. For $N=0$ VOAs, we review the construction of the Fock space $V_L$ from an even lattice $L$ and provide an algebraic description of the Lie algebra $g_{II_{25,1}}$ from the perspective of $24$ different Niemeier lattices $N$ via the decomposition $II_{25,1} = N \oplus II_{1,1}$ using the no-ghost theorem. For $N=1$ SVOAs we review the construction of the Fock space $V_{NS}$ and provide an explicit basis for the spectrum-generating algebra of the Lie algebra $g_{NS}$. For $N=2$ SVOAs, we describe the structure of $g^{(2)}_{NS}$ explicitly …

On The Galois Action On Motivic Fundamental Groups Of Punctured Elliptic And Rational Curves, Nikolay Malkin

Yale Graduate School of Arts and Sciences Dissertations

The main motive of this thesis is to study the action of the motivic Galois group on the motivic fundamental group of an algebraic curve X punctured at a finite set of points. The algebraic, geometric, and analytic aspects of this action are examined in two cases: for X=P1 and for X an elliptic curve. To study this action, we rely on motivic correlators, canonical elements in the fundamental Lie coalgebra of the category of mixed motives over a number field. We trace three themes: (1) The Lie coalgebra structure on the motivic correlators. Using combinatorial arguments with an injection …

Raising The Awareness Of Somali Families: The Positive Impact Of Dual Language Education On Student Success, Khaleef Warsame

School of Education and Leadership Student Capstone Projects

Studies have found that dual language education is powerful for all learners and particularly essential for the success of first- and second-generation immigrant learners in the United States. The learning model enhances students’ academic achievement, school participation, and healthy identity development. Students proficient in both their heritage language and culture and their new homeland’s dominant culture and language are also more likely to gain higher upward mobility and enjoy advanced cognitive development. While the benefits of dual language education (DLE) are explicitly illustrated in the literature, there are currently no Somali dual language programs found to be existing in Minnesota …

Real-World Learning In Middle School Mathematics, Elizabeth Ackerson

School of Education and Leadership Student Capstone Projects

My research question for my capstone project is: How does incorporating real-world word problems into weekly math curriculum in middle school affect students' learning, engagement, and understanding? I have created a math word problem curriculum, “Word Problem Wednesday”, to be used in my own math classroom to create real-world learning opportunities through problem-solving. I teach 5th-grade math, and I have noticed a lack of understanding of word problems related to problem-solving in the classroom. The curriculum I have developed is based on the need for a curriculum where word problems are purposefully incorporated weekly with meaning while creating understanding. Every …

Instructional Strategies And Rigor: Private School Administrator And Teacher Perspectives On Improving Minnesota’S College Mathematic Readiness, Nichelle Guillaume

Education Doctorate Dissertations

Instructional Strategies and Rigor: Private School Administrator and Teacher Perspectives on Improving Minnesota’s College Mathematic Readiness (May 2021)

This qualitative study explored private high school administrator and teacher perspectives on instructional strategies and rigor to improve Minnesota’s college mathematic readiness. Data collection sources for the study included individual interviews, focus groups, and document review. The study produced four emergent themes from the data collected in the individual interviews and focus groups: (a) Importance of Productive Struggle in Mathematic Instruction; (b) Necessary Balance of Mathematical Conceptual Understanding with Skill Acquisition; (c) Connection of Continuous Assessment to Mathematic Content Mastery and (d) …

Biplanar Crossing Numbers Of Bipartite Graphs, Sydney Miyasaki

Senior Theses

The goal of this thesis is to compute upper and lower bounds on the biplanar crossing numbers of complete bipartite graphs. The concept of a biplanar crossing number was first introduced by Owens (Owens 1971) as an optimization problem in circuit design. To prove upper bounds, we follow a method used by Czabarka et. al. (Czabarka et. al. 2006), in which they start from an optimal drawing of a small bipartite graph and use it to generate drawings of larger bipartite graphs. We explore several possibilities for computing lower bounds. One is using Ramsey theory, via the Bipartite Ramsey Number …

Improving Student Learning And Number Sense Through The Combination Of Cooperative Learning And Number Talks, Timothy Augustin

School of Education and Leadership Student Capstone Projects

This study explores the combination of two pedagogical techniques contributing to the development of mathematical literacy in one sixth grade mathematics class. The techniques involved in this project are cooperative learning, which focuses on the learning environment and Number Talks, which focuses on the development of number sense. This three month study involves implementing cooperative learning groups and instilling Number Talks to one sixth grade class of 20 students daily. For this study, the teacher and students participate in a series of monthly assessments, quantitative and qualitative, that are designed to measure the success of the project. This study intends …