Science and Mathematics Education Commons^™

Mathematics Uncovered Through Action Science, William H. Robertson

William H. Robertson

The Power Of X, Darren B. Glass

Math Faculty Publications

In his recent book, The Math Myth: And Other STEM Delusions, political scientist Andrew Hacker argues, among other things, that we should not require high school students to take algebra.

Part of his argument, based on data some have questioned, is that algebra courses are a major contributor to students dropping out of high school. He also argues that algebra is nothing more than an "enigmatic orbit of abstractions" that most people will never use in their jobs. [excerpt]

Motivation For Mathematics: The Development And Initial Validation Of An Abbreviated Instrument, Kenneth Lee Butler

USF Tampa Graduate Theses and Dissertations

This study outlines the development and initial validation of an abbreviated instrument intended to measure motivation for mathematics of university students in developmental algebra courses. I look across many of the predominant theories on motivation with the aim of representing several of these theories as latent constructs in a single instrument that is short enough to be administered in a reasonable amount of time, but inclusive enough that it could incorporate subscales representing multiple distinct latent factors. This study answers a call by researchers expressing a need to investigate relationships between disparate theories on motivation and is a response to …

Algebraic Content And Pedagogical Knowledge Of Sixth Grade Mathematics Teachers, Mariyam Shahuneeza Naseer

Walden Dissertations and Doctoral Studies

Algebra test scores of the Maldivian students from grade 6 through 12 are the lowest compared to any other area of mathematics. Algebra is a fundamental topic in mathematics and lays the foundation for mathematical reasoning and complex problem-solving. Research shows that strengthening algebra instruction could improve student achievement. This concurrent mixed methods study examined the algebraic content and pedagogical knowledge of 5 sixth grade mathematics teachers who teach in 5 different schools across the Maldives. Shulman's major categories of teacher knowledge and Ball, Thames, and Phelps' domains of mathematical knowledge for teaching guided this study. The research questions examined …

Scaffolding The Mathematical “Connections”: A New Approach To Preparing Teachers For The Teaching Of Lower Secondary Algebra., Christine A. Ormond

Australian Journal of Teacher Education

This paper discusses the results of a three-year mixed methods study into the effectiveness of a mathematics education unit. This was written for both pre-service primary education students and re-training in-service teachers, to prepare them for the teaching of pre-algebra and early algebra. The unit was taught rom 2013 to 2015 inclusively in a School of Education setting of a university in an Australian capital city. Focusing on the Number and Algebra strand in the Australian Curriculum, its purpose was to better prepare some novice teachers through modelling a more coherent approach to mathematics teaching. The unit’s genesis lies in …

Calculators In High School Classrooms, Adam P. Rohrabaugh, Clay M. Cooper

Williams Honors College, Honors Research Projects

In today’s mathematics classrooms, calculators are becoming incredibly well known and used almost daily. However, there has been a common question about the use of these calculators: Is too much exposure to calculators causing students to become dependent on them and consequently start to forget basic addition, subtraction, multiplication, and division, leading into confusion on other mathematics topics because the most basic foundation of mathematics is not there? The purpose of this paper is to discuss both sides of this question by looking at different studies as well as provide our own experiences with this subject while working in different …

The Influence Of Types Of Homework On Opportunity To Learn And Students' Mathematics Achievement: Examples From The University Of Chicago School Mathematics Project, Yiting Yu

USF Tampa Graduate Theses and Dissertations

ABSTRACT

Public views on assigning students mathematics homework have been controversial. Although homework is designed for students to complete during non-school hours (Cooper, 1989), many see homework as excessive pressure on students. Most research placed their focus on the influence of the time spent on homework or the amount of homework on student achievement. Few studies have addressed the impact of types of mathematics homework. The purpose of this study is to examine the role of homework types in influencing opportunity to learn (OTL) on student achievement.

This quantitative study used subsets of a large existing dataset collected by University …

Mat-Rix-Toe: Improving Writing Through A Game-Based Project In Linear Algebra, Adam Graham-Squire, Elin Farnell, Julianna Stockton

Elin R Farnell

The Mat-Rix-Toe project utilizes a matrix-based game to deepen students’ understanding of linear algebra concepts and strengthen students’ ability to express themselves mathematically. The project was administered in three classes using slightly different approaches, each of which included some editing component to encourage the improvement of the students’ mathematical thinking and writing. Differences in the implementation of the project illustrate the benefits and drawbacks of various methods of editing in the mathematics classroom and highlight recommendations for improvements in future implementations of the project.

Algebra 1 Students’ Ability To Relate The Definition Of A Function To Its Representations, Sarah A. Thomson

Electronic Theses, Projects, and Dissertations

One hundred high school Algebra students from a southern California school participated in this study to provide information on students’ ability to relate the definition of function to its representations. The goals of the study were (1) to explore the extent to which students are able to distinguish between representations of functions/non-functions; (2) to compare students’ ability to distinguish between familiar/unfamiliar representations of functions/non-functions; (3) to explore the extent to which students are able to apply the definition of function to verify function representations; and (4) to explore the extent to which students are able to provide an adequate definition …

The Skatepark Mathematics Extravaganza, William H. Robertson

William H. Robertson

Examining Implementations Of Blended Learning In A K-12 Mathematics Classroom, Kelsey Waynick

Honors Projects

In this research project, I investigated the effects on eighth grade students’ performances and perceptions throughout a blended learning experience by implementing a combination of face-to-face and online instructional strategies in an Algebra classroom. This blended experience was segmented into two units – a face-to-face unit and a blended unit – to allow for comparison within the participant group of high-achieving mathematics students. Edmodo, an online educational platform, was utilized to provide students with access to online resources at home during the blended unit. Students completed a series of three identical tests to quantitatively measure learning growth at designated checkpoints …

Exploring Similarities Between Instruction In Grade 7 Ela And Mathematics Classrooms, And The Possible Benefits Of Interdisciplinary Instructional Comprehension Strategies, Danielle Caron

Honors Program Theses and Projects

This study took place in an English language arts (ELA) and mathematics classrooms at a suburban junior high school in southeastern Massachusetts. Surveys indicated that mathematical problems elicit nervousness more often than reading assignments do, and mathematical vocabulary is harder for students to understand than vocabulary of other subject. This research focused on integrating reading comprehension-strategies of vocabulary integration, graphic organizers, and visual aids within a mathematics curriculum to combat student apprehension. The purpose of this study was to provide evidence-based, interdisciplinary mathematics and ELA lesson plans in alignment with Common Core Standards to a seventh grade algebra class. Pre-assessment …

Teaching Algebra: A Comparison Of Scottish And American Perspectives, Brittany Munro

Undergraduate Honors Theses

A variety of factors influence what teaching strategies an educator uses. I analyze survey responses from algebra teachers in Scotland and Appalachia America to discover how a teacher's perception of these factors, particularly their view of mathematics itself, determines the pedagogical strategies employed in the classroom.

Relationships Between The Algebraic Performance Of Students In Subject-Specific And Integrated Course Pathways, Derrick Saddler

USF Tampa Graduate Theses and Dissertations

The purpose of this study was to compare the algebraic performance gains of high school students who enroll in an integrated mathematics course pathway (i.e., Integrated Mathematics I-II-III) to the algebraic performance gains of high school students who enroll in a subject-specific course pathway (i.e., Algebra I-Geometry-Algebra II). Several studies have been performed in which researchers examined relationships between mathematics outcomes and the course-taking patterns of high school students enrolled in subject-specific course pathways. However, there is little extant research in which researchers have investigated effects of content organization on students' learning and achievement. Therefore, this study addresses calls for …

Faculty Viewpoints On Teaching Quantway®, Heather Howington, Thomas Hartfield, Cinnamon Hillyard

Numeracy

Quantway is a quantitative reasoning-based pathway for developmental math that has been developed as an alternative to the traditional remedial algebra sequence. To explore the experiences of faculty involved with Quantway, we interviewed eight individuals who have taught the course in the past year to survey their attitudes and opinions about students in their classes, the materials and pedagogies in use, and the collegial interaction of networked faculty. Faculty were selected with the intention of gathering a broad set of opinions resulting from differences of location, experience, and other factors. In this paper, we summarize those interviews by identifying common …

Success After Failure: An Examination Of Credit Recovery Options And Their Effect On College- And Career-Readiness, Kathryn B. Johnson

Theses and Dissertations--Science, Technology, Engineering, and Mathematics (STEM) Education

More than ever before, educators and researchers are keeping a keen eye on student college- and career-readiness. The widely adopted Common Core State Standards were written with the explicit goal of helping students to be college- or career-ready by the time they graduate from high school. However, many students experience setbacks, such as course failure, within their educational career placing them at risk for not reaching this goal. Because the ACT can predict student success in college, states often use benchmark scores from the exam to measure student college- and career-readiness. A student who fails to learn fundamental concepts in …

Pathways To Professional Growth: Investigating Upper Primary School Teachers’ Perspectives On Learning To Teach Algebra, Karina J. Wilkie, Doug Clarke

Australian Journal of Teacher Education

This paper discusses upper primary school teachers’ perspectives on changes to their knowledge and practice through participation in a design-based research project. It analyses their experiences using Clarke & Hollingsworth’s (2002) empirically-founded model for professional growth to understand more about the mechanisms for change that might support teachers in learning to teach a challenging but important aspect of mathematics – algebra. Ten teachers were involved in cycles of collaborative planning, team-teaching, evaluating, and revising five lessons for their classes on developing functional thinking through pattern generalisation over one year. The teachers referred to observations of teaching in action, and modification …

The Influences Of Mathematics Self-Efficacy, Identity, Interest, And Parental Involvement On Stem Achievement In Algebra For Female High School Students, Nicol R. Howard

Educational Studies Dissertations

The purpose of this study was to determine the predictability of STEM achievement in Algebra for female high school students utilizing mathematics self-efficacy, mathematics interest, mathematics identity, and parental involvement. This study employed data from the High School Longitudinal Study of 2009 (HSLS:09/12) which consisted of 3,938 female eleventh-grade participants randomly selected from 944 public and private high schools during the fall 2009 academic year. The results of a hierarchical multiple regression indicated that mathematics identity was the strongest predictor of STEM achievement for female high school students, regardless of race. In spite of this significant relationship, STEM achievement outcomes …

The Effects Of A Varied Method Of Instruction On Student Achievement, Transfer, Situational Interest, And Course Retention Rates In Community College Developmental Mathematics, Kevin L. Mccandless

Doctoral Dissertations

The purpose of this quasi-experimental study was to compare the effects of a varied method of instruction on student achievement, knowledge transfer, situational interest, and course retention rates, relative to a non-varied method of instruction, in community college developmental mathematics. The varied method of instruction consisted of active learning teaching practices with foundations in social constructivism, whereas the non-varied method of instruction was founded in Cognitive Load Theory and consisted primarily of explicit instruction and individual practice.

An initial sample of 139 students who enrolled in six sections of Beginning Algebra at an urban community college in Northern California participated …

Effects Of Embedded Study-Skills Instruction On High School Students' Attitudes Toward Mathematics, Alberta Diahann Banks

Walden Dissertations and Doctoral Studies

The target school used embedded study skills in Algebra I classes to improve attitudes toward mathematics. The purpose of this sequential, explanatory mixed-methods study was to examine the effect of embedded study-skills instruction on students' attitudes toward mathematics. Metacognitive theory was used for this study's framework. Participants were 28 Grade 9 and 10 students who repeated Algebra I. Quantitative data from the Attitudes Toward Mathematics Inventory assessed students' pre- and post-instruction attitudes toward mathematics in 4 domains. Data were analyzed using 4 independent samples t tests for students who did and did not receive embedded instruction. Qualitative data were collected …

Mathematics Achievement With Digital Game-Based Learning In High School Algebra 1 Classes, Terri Ferguson

Doctoral Dissertations and Projects

This study examined the impact of digital game-based learning (DGBL) on mathematics achievement in a rural high school setting in North Carolina. A causal comparative research design was used in this study to collect data to determine the effectiveness of DGBL in high school Algebra 1 classes. Data were collected from the North Carolina End-of-Course (EOC) Test for high school Algebra 1. The data collection was broken down by comparison groups based on academic achievement as measured by the North Carolina EOC Test for Algebra 1. The comparison groups were student participants who received digital game-based instruction and tradition instruction …

Cartooning In Algebra And Calculus, Lauren Jeneva Moseley Ph.D.

Lauren Jeneva Moseley

This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students’ conceptual understanding.

An Investigation Of Factors Affecting Student Performance In Algebraic Word Problem Solutions, Jerry Eugene Wright

Education Dissertations and Projects

This dissertation was designed to investigate the potential significance of several student algebraic word problem solving skills. The solution of an algebra word problem (AWP) requires the creation and solution of an equation based on the problem context. Common Core State Standards in both English Language Arts and Mathematics emphasize student learning and proficiency in algebra word problem contexts. Eight factors of student mathematical ability were proposed, and three of those eight factors were studied in depth to determine their significance. Similar research supported the theory that the translation phase of the solution process presented the student with the most …

Teaching Algebra Through Functional Programming:An Analysis Of The Bootstrap Curriculum, Robert Lee

Theses and Dissertations

Bootstrap is a computer-programming curriculum that teaches students to program video games using Racket, a functional programming language based on algebraic syntax. This study investigated the relationship between learning to program video games from a Bootstrap course and the resulting effect on students' understanding of algebra. Courses in three different schools, lasting about six weeks each, were studied. Control and treatment groups were given a pre and post algebra assessment. A qualitative component consisting of observations and interviews was also used to further triangulate findings. Statistical analysis revealed that students who completed the Bootstrap course gained a significantly better understanding …

An Investigation Of Palindromes And Their Place In Mathematics, Ryan Andrew Nivens

ETSU Faculty Works

What do the Honda Civic, the Mazda 626, and the Boeing 747 have in common? What about Weird Al's song Bob, the first name of Miley Cyrus' alter ego, and the 70s sensation Abba? What do all these things have in common? They all contain palindromes. While some people recognise a palindrome when they see one, fewer realise that a palindrome is a special case of a pattern and that these patterns are all around. Palindromes frequently occur in names, both of vehicles and people, and in music.

The Impact Of Teachers' Characteristics And Self-Reported Practices On Students' Algebra Achievement, Liza Cope

Legacy Theses & Dissertations (2009 - 2024)

This study examined the impact of teachers' characteristics and self-reported practices on students' Algebra achievement while controlling for students' characteristics. This study is based on the secondary analysis of data collected from a nationally representative sample of 9th grade students and their mathematics teachers during the base year of the High School Longitudinal Study of 2009 (HSLS). Student and teacher data were obtained through questionnaires and students' Algebra achievement was measured by an ability-adaptive assessment designed to measure a cross-section of understandings representative of the six major Algebraic content domains (The language of algebra; Proportional relationships and change; Linear equations, …

Investigating The Impact Of Interactive Applets On Students’ Understanding Of Parameter Changes To Parent Functions: An Explanatory Mixed Methods Study, Robin R. Mcclaran

Theses and Dissertations--Science, Technology, Engineering, and Mathematics (STEM) Education

The technology principle in the Principles and Standards for School Mathematics (NCTM, 2000) states that technology plays an important role in how teachers teach mathematics and in how students learn mathematics. The purpose of this sequential explanatory mixed-methods study was to examine the impact of interactive applets on students’ understanding of parameter changes to parent functions. Students in the treatment classes were found to have statistically significantly higher posttest scores than students in the control classes. Although the data analysis showed a statistically significant difference between classes on procedural understanding, no statistically significant difference was found with regard to conceptual …

The Mathematics Of Skateboarding: A Relevant Application Of The 5es Of Constructivism, William H. Robertson

William H. Robertson

Attending High School Algebra I: In Search Of Well-Managed, Engaging, Culturally Relevant, And Caring Classrooms, Cassandra Dunn Gannett

Electronic Theses and Dissertations

The inequities in learning between the rich and the poor have become pervasive in United States. This is evidenced by the high school graduation rates, college attendance percentages, and employment statistics. Upon another wave of reform, the Common Core State Standards in mathematics are currently being adopted in hopes of increasing learning for all students, with a focus on college and career readiness. This study is intent on finding ways to remedy the inequities in mathematics between the high income and low income schools by focusing on one of the great glass ceilings to high school graduation and beyond, high …

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 …