Science and Mathematics Education Commons^™

Exploring The Knowledge Of Algebra For Teaching., Jonathan David Watkins

Electronic Theses and Dissertations

For the past few decades, researchers in mathematics education have been exploring the concept of pedagogical content knowledge (PCK)—or knowledge related to teaching content—and applying it to various areas of mathematics, such as algebra. Research related to teacher knowledge of algebra is critical because researchers (e.g., Hill, Rowan, & Ball, 2005) have found correlations between some types of teacher knowledge and student achievement in mathematics; students from around the world are outperforming U.S. students on international assessments of mathematics, including algebra (Organization for Economic Cooperation and Development, 2014, 2016); and algebra plays an integral role in the K-12 mathematics curriculum …

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 …

Exploring Authenticity Through An Engineering-Based Context In A Project-Based Learning Mathematics Activity, Bradley Bowen, Bryanne Peterson

Journal of Pre-College Engineering Education Research (J-PEER)

As education works to reconnect student learning to something more than standardized testing, project-based learning (PBL) has become a popular way to increase student engagement while providing more authentic applications of student knowledge. While research regarding PBL is bountiful, little has been done to connect this body of research with student perceptions regarding its classroom application, especially concerning authenticity and student engagement. This research focuses on the topic of ‘‘task authenticity’’ as a means to improve student outcomes. Two groups of seventh-grade students were presented the concept of slope and y-intercept in the context of engineering-based activities. The research …

Between Paralysis And Empowerment: Action In Mathematics For Social Justice Work, Lidia Gonzalez

Publications and Research

In this article, I focus on my experiences teaching a seminar in critical pedagogy and the math for social justice (MfSJ) work that grew from of my students’ reflections as to how they might promote change towards justice. The course was designed to acquaint students with the research literature in critical pedagogy as we explored the social, political, cultural, and economic realities around our system of public education. Yet there came a point where students questioned the value of such exploration as they genuinely considered what to do next. I, too, struggled both to support the students I was working …

Actualizing The Rights Of The Learner: The Role Of Pedagogical Listening, Allison Hintz, Kersti Tyson, Andrea R. English

Democracy and Education

This response to Crystal Kalinec-Craig’s article on the Rights of the Learner (RotL) aims to take up and build on the author’s ideas about how the RotL framework can promote equitable mathematics teaching and learning. Specifically, this response examines how listening is implied in the work of teachers who support young mathematicians as they exercise their rights to be confused, claim mistakes, and say and write what makes sense. In doing so, we seek to highlight some of the opportunities and challenges that can emerge for teachers attempting to support all learners to actualize these rights.

The Demands Of The Rights Of The Learner, Elham Kazemi

Democracy and Education

In this response to Kalenic-Craig’s (2017) article, “The Rights of the Learner: A Framework For Promoting Equity through Dynamic Formative Assessment,” I consider what implications the RotL framework has for the work that teachers and students must do in learning environments where these rights flourish. The RoTL emphasizes student sensemaking and communication in the classroom. Given the realities of classrooms as racialized, gendered, and classed spaces, this emphasis on communication demands critical consciousness for both teachers and students.

Examining Ec-6 Pre-Service Teachers' Perceptions Of Self-Efficacy In Teaching Mathematics, Tonya D. Jeffery, Lisa D. Hobson, Sarah J. Conoyer, Karen E. Miller, Lesley F. Leach

Faculty Publications

Mathematics teacher quality has become a major focus in national education reform efforts. In addition, there is an increasing interest in the effectiveness of teacher preparation programs and the undergraduate preparation of elementary mathematics teachers. Empirical evidence suggests that teacher attitudes, behaviors and values, or dispositions, towards teaching have a significant impact on student outcomes. The purpose of this study is to survey juniors and seniors in an undergraduate teacher preparation program to gauge their perceptions of self-efficacy and comfort with teaching mathematics. The results have implications for, and reaffirm concerns about the undergraduate preparation of elementary mathematics teachers.

Six Propositions Of A Social Theory Of Numeracy: Interpreting An Influential Theory Of Literacy, Jeffrey Craig, Lynette Guzmán

Numeracy

We share our experiences comprehending social theory as it applies to numeracy scholarship. We build on existing arguments that social theory—explicitly acknowledging the presence and influence of histories, power, and purposes—offers something important to scholars who study and discuss numeracy. In this article, we translate the six propositions of one particular social theory of literacy into propositions about numeracy, then we explore the meaning of each proposition, its connections to existing scholarship, and its implications. This article emerges from two literature reviews: one on social theories (especially their application to and development in literacy) and one on numeracy. We bring …

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 …

Collaboration Among Mathematicians And Mathematics Educators: Working Together To Educate Preservice Teachers, Amanda R. Mohn

USF Tampa Graduate Theses and Dissertations

Collaboration among higher education professors who are responsible for the education of preservice teachers is one potential solution to the problem of poor teacher preparation. Specifically, collaboration among mathematics educators and mathematicians can enhance preservice teacher preparation because it provides opportunities for preservice teachers to develop pedagogical content knowledge. However, collaborative efforts are challenging, and collaborators often face obstacles and tensions arise among the collaborative group members. Learning about ways the collaborators approach their collaborative efforts, the issues and tensions that arise, the hindering and supporting factors that affect the collaboration, and the potential outcomes of collaborative efforts provides information …

“Indefensible, Illogical, And Unsupported”; Countering Deficit Mythologies About The Potential Of Students With Learning Disabilities In Mathematics, Rachel Lambert

Education Faculty Articles and Research

This paper describes two myths that circulate widely about the potential of students with Learning Disabilities to learn mathematics: (1) that students with Learning Disabilities cannot benefit from inquiry-based instruction in mathematics, and only from explicit instruction; and (2) that students with Learning Disabilities cannot construct their own mathematical strategies and do not benefit from engaging with multiple strategies. In this paper, I will describe how these myths have developed, and identify research that counters these myths. I argue that these myths are the unintended consequences of deficit constructions of students with Learning Disabilities in educational research. Using neurodiversity to …

Tinkering With Logo In An Elementary Mathematics Methods Course, Keri Duncan Valentine

Interdisciplinary Journal of Problem-Based Learning

With an increased push to integrate coding and computational literacy in K–12 learning environments, teacher educators will need to consider ways they might support preservice teachers (PSTs). This paper details a tinkering approach used to engage PSTs in thinking computationally as they worked with geometric concepts they will be expected to teach in K–5. Experiences programming in Logo to construct authentic artifacts in the form of two-dimensional geometric graphics not only supported PSTs’ understanding of core geometric and spatial concepts, but also helped them to make connections between mathematics and computational literacy. Artifacts and discourse are discussed as they relate …

How Readability Factors Are Differentially Associated With Performance For Students Of Different Backgrounds When Solving Mathematics Word Problems, Candace Walkington, Virginia Clinton, Pooja Shivraj

Educational Foundations and Research Faculty Publications

The link between reading and mathematics achievement is well known, and an important question is whether readability factors in mathematics problems are differentially impacting student groups. Using 20 years of data from the National Assessment of Educational Progress and the Trends in International Mathematics and Science Study, we examine how readability factors – such as length, word difficulty, and pronouns – interact with student background characteristics – such as race/ethnicity, mathematics achievement, and socioeconomic status. Textual features that make problems more difficult to process appear to differentially negatively impact struggling students, while features that make language easier to process appear …

Parts Of The Whole: Hands On Statistics, Dorothy Wallace

Numeracy

In this column we describe a hands-on data collection lab for an introductory statistics course. The exercise elicits issues of normality, sampling, and sample mean comparisons. Based on volcanology models of tephra dispersion, this lab leads students to question the accuracy of some assumptions made in the model, particularly regarding the normality of the dispersal of tephra of identical size in a given atmospheric layer.

Why I Believe People Need Painting By Numbers, Jason Makansi

Numeracy

Jason Makansi.2016. Painting By Numbers: How to Sharpen Your BS Detector and Smoke Out the Experts (Tucson AZ: Layla Dog Press). 196 pp. ISBN 978-0998425900.

This piece briefly introduces my Painting By Numbers, which aims to take the core messages of the QL/QR community from academic and professional circles to the rest of the citizenry. I describe the book in the context of the critical need for the most basic numeracy tools to help consumers of news, information, and analysis—delivered through traditional and contemporary social media outlets—determine where a reported numerical result lies on the scale from utter nonsense …

Disrupting Dominant Discourses: A (Re)Introduction To Social Practice Theories Of Adult Numeracy, Helen M. Oughton

Numeracy

The role of dominant discourse in constructing a deficit view of adult numeracy is examined, using reports from recent international surveys of adult skills as illustrative examples. Social practice theory is introduced as an alternative perspective for examining the ways adults actually use numeracy in their daily lives and work. This perspective suggests the test items used by large-scale surveys such as PIACC are only proxies for real-life numeracy skills, and that performance in such tests may misrepresent the numeracy skills of adults. Instead, social practice theory suggests that adults may have informal, situated numeracy practices that serve them adequately …

The Impact Of Tracking Students In Mathematics On Middle School Student Achievement Outcomes, David P. Glasner

ETD Archive

The purpose of this study was to explore whether and how tracking structures in mathematics courses at the middle school level relate to differences in achievement between white and black students. This study used propensity score matching to compare the achievement outcomes of students enrolled in advanced mathematics classes, with students of comparable ability and background enrolled in grade-level math classes. The study sample was comprised of 1,510 students. Results from the study show that enrollment in an advanced-math course was associated with statistically significant improvement in math achievement for average-ability students. In addition, study results show that increases in …

Seeing Mathematics Through Different Eyes: An Equitable Approach To Use With Prospective Teachers, Christa Jackson, Cynthia E. Taylor, Kelley Buchheister

Department of Child, Youth, and Family Studies: Faculty Publications

Teacher educators need to prepare prospective teachers by encouraging them to critically examine their current beliefs about the teaching and learning of mathematics while also providing opportunities for prospective teachers to develop an equity-centered orientation. Attending to these practices in teacher preparation programs may help prospective teachers observe actions that occur in classrooms and determine effective strategies that provide the opportunity to enhance all students’ access to high-quality mathematics instruction. As mathematics teacher educators, we must recognize what prospective teachers attend to as they direct their attention to various classroom events and how they relate the events to broader principles …

Improving Mathematical Skill: The Perceptions Of Rural Minnesota Mathematics Educators, Michael Haskins

All Graduate Theses, Dissertations, and Other Capstone Projects

This qualitative phenomenological study is focused on the perceptions of mathematics educators on how to improve mathematical skill in high school students. The main purpose was to describe, recognize, and interpret the lived experience that have allowed educators to achieve the best results for their students. The population for the current study was mathematics educators that were located in a rural Southwest Minnesota city with medium population. These educators were either college educators or middle and high school teachers. The measures that were used to select the participants for the study were that they must hold at least a bachelor's …

Effects Of The Instruction With Mathematical Modeling On Pre-Service Mathematics Teachers’ Mathematical Modeling Performance, Gulzade Karaci Yasa, Ilhan Karatas

Australian Journal of Teacher Education

The purpose of the study was to investigate the effects of the instruction with mathematical modeling on pre-service mathematics teachers’ mathematical modeling performance. The participants were 24 pre-service elementary mathematics teachers. A mixed method approach was used to conduct the research. Each week, the participants were given two mathematical modeling problems and solved them as a group. After that, each group shared their solutions with the class so that there was an opportunity to focus on different solution methods. The data was collected via a pre and a post mathematical modeling test. SPSS package program was utilized in order to …