Education Commons^™

Pre-Service Elementary Teachers' Use Of Spatial Diagrams: Investigations Of Unbounded Shearing On Solid Figures, Camden G. Bock

Electronic Theses and Dissertations

Mithala and Balacheff (2019) describe three difficulties with two-dimensional representations of three-dimensional geometrical objects: “it is no longer possible to confuse the representation with the object itself,” visually observed relationships can be misleading, and analysis of the representation requires the use of lower-dimensional theoretical properties. Despite these difficulties, students are routinely expected to learn about three-dimensional figures through interacting with two-dimensional inscriptions. Three-dimensional alternatives include diagrams realized through various spatial inscriptions (e.g., Dimmel & Bock, 2019; Gecu-Parmaksiz & Delialioglu, 2019; Lai, McMahan, Kitagawa & Connolly, 2016; Ng and Sinclair, 2018). Such diagrams are three-dimensional in the sense that they occupy …

Elementary Statistics Instructors' Uptake Of The Teaching Practices Recommended By The American Statistical Association, Marisol Sanchez Cortez

Theses and Dissertations

Previous studies point out there has been a wide gap, in the teaching of mathematics, between the practices recommended in the credential programs and the practices teachers actually do. The purpose of this study is to explore how consistent the teaching practices of introductory statistics instructors are to the recommendations endorsed by the American Statistical Association, to understand what their attitudes to the gap are, and to identify the factors that prevent the instructors from implementing the recommended practices. Data were collected from nine statistics instructors at a state university through survey, classroom observations, and interviews. Findings indicate that the …

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 …

Mentoring Future Mathematics Teachers: Lessons Learned From Four Mentoring Partnerships, Angie Hodge, Janice Rech, Michael Matthews, Kelly Gomez Johnson, Paula Jakopovic

Teacher Education Faculty Publications

Mentoring is an important aspect of mathematics teacher education, and in particular, pre-service teacher education. Faculty at a large Midwestern university developed and refined a mentoring program designed to help pre-service secondary mathematics teachers, called Scholars, become future leaders in mathematics education. This paper describes how faculty mentors leveraged challenges in the mentoring program’s early stages based on their reflections and initial mentee outcomes to create a more effective mentoring program. Recommendations based on research and practice are provided for other university programs interested in mentoring future mathematics teachers.

Cognitive, Neural, And Educational Contributions To Mathematics Performance: A Closer Look At The Roles Of Numerical And Spatial Skills, Zachary C.K. Hawes

Electronic Thesis and Dissertation Repository

The principal aims of this thesis were to (1) provide new insights into the cognitive and neural associations between spatial and mathematical abilities, and (2) translate and apply findings from the field of numerical cognition to the teaching and learning of early mathematics.

Study 1 investigated the structure and interrelations amongst cognitive constructs related to numerical, spatial, and executive function (EF) skills and mathematics achievement in 4- to 11-year old children (N=316). Results revealed evidence of highly related, yet separable, cognitive constructs. Together, numerical, spatial, and EF skills explained 84% of the variance in mathematics achievement (controlling for chronological age). …

Secondary Mathematics Teachers’ Responses To Pivotal Teaching Moments, Kami M. Dupree

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This study used a multiple case study design to explore the occurrence of pivotal teaching moments, teachers’ responses to these moments, and teachers’ own perceptions of the impact of these moments on their own knowledge development. The participants were six practicing secondary mathematics teachers. The researcher collected data from teacher created lesson plan outlines, observations of the same lesson delivered to two different classes, participant interviews, and teacher reflection journals. The researcher reviewed the lesson plan outlines prior to observations to understand teachers’ anticipations. During observations, the researcher recorded observed pivotal teaching moments, corresponding teacher responses to these moments, and …

The Relationship Between English Language Learners’ Mathematics Problem Solving Strategies And The Mathematics Register, Sarah Reeves Frederickson

Graduate Theses and Dissertations

This case study followed three Hispanic and three Marshallese students’ participation in a seventh grade pre-algebra unit over the course of four weeks. Pre-assessment items indicated that the students had difficulty with aspects of the mathematics register. Their teacher employed an interpretation of the gradual release model of instruction in which direct strategies for translating word problems into equations with unknowns were modeled prior to students doing similar problems on their own. In these situations, students showed some success in solving similar problems. However, post-assessment results indicated that none of the six students were able to successfully solve open response …

Mathematics Out Of Nothing: Talking About Powerful Mathematical Ideas With Children, Matthew Oldridge

Journal of Humanistic Mathematics

Parents and educators have powerful opportunities to introduce children to big mathematical ideas, when those ideas become necessary. Children are capable and curious. They don’t need to be sheltered from big mathematical ideas. Bring out mathematical ideas when kids are ready, or when they are needed. This article describes one such instance, when I helped my six-year-old son move beyond zero in the negative direction when subtracting.

Visual Teaching Of Geometry And The Origins Of 20th Century Abstract Art, Stephen Luecking

Journal of Humanistic Mathematics

As a group, the artists educated near the turn of the 19^th and 20^th centuries possessed greater mathematical knowledge than expected of artists today, especially regarding constructive skills in Euclidean geometry. Educational theory of the time stressed such skills for students in general, who needed these to enter the workplace of the time. Mathematics teaching then stressed the use of manipulatives, i.e., visual and interactive aids thought to better fix the student’s acquisition of mathematical skills. This visual training, especially in geometry, significantly affected the early development of abstraction in art. This paper presents examples of this visual …

Full Issue: Journal On Empowering Teaching Excellence, Volume 3, Issue 1, Kim Hales

Journal on Empowering Teaching Excellence

The full Spring 2019 issue (Volume 3, Issue 1) of the Journal on Empowering Teaching Excellence, Spring 2019

Parts Of The Whole: Logical Categories Of Learning: Why Teaching Qr Is Hard, Dorothy Wallace

Numeracy

This column introduces the reader to an essay by anthropologist Gregory Bateson on the nature of learning. In that essay, he stratifies the learning process into categories based on what aspect of the student’s understanding is required to change in order to accomplish a given learning task. A discussion of the first three categories is followed here by examples from quantitative reasoning tasks and a further example from the ongoing discussion in the community of what numeracy entails. Bateson’s classification of learning into “logical categories” sheds light on what the goals of numeracy ask of both student and teacher, as …

A Comparison Study Of Using Origami As A Teaching Tool In Middle-School Mathematics Class In North America And China, Yueying Liu

Major Papers

This Major Paper compares origami-based mathematics school activities in North America and China. It introduces the current situation of the use of origami in mathematics classes to identify the similarities and differences of using origami as a teaching approach in these two regions. The Paper also attempts the analysis from various perspectives, including mathematics reform, mathematics learning system and environment, as well as the benefits of using origami in mathematics class, and how it relates to students’ mathematics achievement. Both North American and Chinese mathematics educators’ focus on integrating origami into middle schools’ mathematics classes can be found in the …

Fragile Strength: Math Self-Efficacy Of High Achieving Girls, Tristan Tang

Education | Master's Theses

Math gender gap research shows girls’ math self-efficacy to be correlated with their interest in pursuing higher levels of math education and STEM career opportunities. Most math gender gap studies have used only quantitative approaches, thereby missing the opportunity to gain deeper perspectives directly from girls who are steadfastly facing the math gender gap. This study centered around two small focus groups of girls attending a unique secondary school where every afternoon is fully dedicated to deep engagement with higher-level mathematics. Additionally, parents of girls at the school were surveyed to provide further insight into possible sources of their daughter’s …

Does Teaching The History Of Mathematics In High School Aid In Student Understanding?, Anne Campbell

Undergraduate Honors Thesis Projects

This research will study the effect teaching the history of mathematics in a high school classroom has on student understanding. To accomplish this, lessons both including and excluding historical background on different topics were taught in an Honors Algebra 2 class in the high school setting. This research aims to engage student learning and investigation of topics that normally do not draw a lot of student focus and spark a new or revived interest in mathematics for students by broadening lessons to include material of which students would not otherwise be exposed. The lessons themselves aim to engage other current …

“Diabesity” Among Latinos: A Culturally Relevant Mathematics Activity By A Mathematics Teacher Candidate, Olga Ramirez, Cherie Mccollough

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

This paper summarizes a culturally relevant mathematics project conducted by a mentored secondary-level Latino teacher candidate (TC) as a requirement for an undergraduate mathematics project course at a south Texas university. The culturally relevant math project involved four secondary Latino students and their parents. The topic was “diabesity”; that is, diabetes and obesity among Latinos southern region in the United States of America with an emphasis on body mass index, proper diet, and exercise. Remarks by the faculty mentor and a faculty consultant about the TC work and reflections regarding this project are also included and provide perspectives on how …

Critical Mathematical Inquiry

Occasional Paper Series

Welcome to Issue 41 of Bank Street’s Occasional Paper Series. The issue features a collection of papers by authors with a shared affinity for the work of critical mathematical inquiry (CMI). In what follows, we present our framing of mathematics education as a participatory venue for CMI and situate it in the context of another, perhaps more familiar approach to teaching mathematics for social justice (TMfSJ).

The “Soft Bigotry Of Low Expectations” And Its Role In Maintaining White Supremacy Through Mathematics Education, Laurie Rubel, Andrea V. Mccloskey

Occasional Paper Series

In this study, we offer an analysis of the phrase the "soft bigotry of low expectations" and considers its role in rhetoric about U.S. mathematics education policy and practice, especially in regards to Critical Mathematical Inquiry. From the phrase’s origins in a speech given by President George W. Bush in 2000, to its current use on social media, this phrase offers a lens into white supremacy and "tools of whiteness" (Picower, 2009), and their persistence in U.S. schooling paradigms, especially about mathematics. We analyze specific, recent instantiations of the phrase on blogrolls and Twitter, in addition to more implicit …

Collaboration And Critical Mathematical Inquiry: Negotiating Mathematics Engagement, Identity, And Agency, Frances K. Harper

Occasional Paper Series

When faced with the challenge of supporting students to do the “messy” mathematical work necessary for exploring social justice problems through critical mathematical inquiry, teachers might rely on more procedural or direct instruction. Because how students learn matters as much as what they learn, this can inadvertently limit students’ engagement with mathematics. Instructional strategies designed to foster equitable collaboration can support critical mathematical inquiry by promoting norms for equitable student engagement and mathematics identity development. As teachers and students negotiate what counts as mathematics engagement and who has access to mathematics, students’ authority over mathematics and social justice issues increases.

Cultivating A Space For Critical Mathematical Inquiry Through Knowledge-Eliciting Mathematical Activity, Debasmita Basu, Steven Greenstein

Occasional Paper Series

Learning mathematics becomes more effective when teachers leverage their students' mathematical and everyday knowledge as resources for instruction. Thus, tasks that reveal these forms of knowledge would be especially useful to teachers. Unfortunately, such tasks are hard to find and even harder to create. Consequently, we developed a collection of mathematical tasks that we hoped would elicit “children’s multiple mathematical knowledge bases (i.e., the understandings and experiences that have the potential to shape and support children’s mathematics learning—including children’s mathematical thinking, and children’s cultural, home, and community-based knowledge)” (Turner et al., 2012, p. 68). These tasks proved to be productive …

Symmetry And Measuring: Ways To Teach The Foundations Of Mathematics Inspired By Yupiaq Elders, Jerry Lipka, Barbara Adams, Monica Wong, David Koester, Karen Francois

Journal of Humanistic Mathematics

Evident in human prehistory and across immense cultural variation in human activities, symmetry has been perceived and utilized as an integrative and guiding principle. In our long-term collaborative work with Indigenous Knowledge holders, particularly Yupiaq Eskimos of Alaska and Carolinian Islanders in Micronesia, we were struck by the centrality of symmetry and measuring as a comparison-of-quantities, and the practical and conceptual role of qukaq [center] and ayagneq [a place to begin]. They applied fundamental mathematical principles associated with symmetry and measuring in their everyday activities and in making artifacts. Inspired by their example, this paper explores the question: Could symmetry …

The Mathematics Orientation Seminar: A Tool For Diversity And Retention In The First Year Of College, Salvatore J. Petrilli

Journal of Humanistic Mathematics

In this article I describe Adelphi University's Mathematics Orientation Seminar, a new course that was introduced into the mathematics major to help students find their passion in mathematics and to strengthen the educational community within our department. I discuss quantitative and qualitative results of surveys among students in the Mathematics Orientation Seminar in Fall 2016 and Fall 2017, which suggest that this might be a useful course for other institutions to utilize within any major. Finally, I explore faculty perspectives and describe what I believe to be the final version of this course.

Disciplinary Learning From An Authentic Engineering Context, Catherine Langman, Judith Zawojewski, Patricia Mcnicholas, Ali Cinar, Eric Brey, Mustafa Bilgic, Hamidreza Mehdizadeh

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

This small-scale design study describes disciplinary learning in mathematical modeling and science from an authentic engineeringthemed module. Current research in tissue engineering served as source material for the module, including science content for readings and a mathematical modeling activity in which students work in small teams to design a model in response to a problem from a client. The design of the module was guided by well-established principles of model-eliciting activities (a special class of problem-solving activities deeply studied in mathematics education) and recently published implementation design principles, which emphasize the portability of model-eliciting activities to many classroom settings.

Two …

We Would If We Could: Examining Culturally Responsive Teaching Self-Efficacy In A Middle School Mathematics Methods Course, Jamaal R. Young, Jemimah L. Young, Brandon L. Fox, Earl R. Levingston Jr., Alana Tholen

Faculty Publications

Despite mounting evidence of the pedagogical importance of culturally responsive teaching, many teachers do not implement culturally responsive practices in their classrooms. The purpose of this study was to investigate pre-service mathematics teachers’ culturally responsive teaching and outcome expectancy in order to inform teacher preparation in mathematics methods courses. Participants completed the Culturally Responsive Teaching Self-efficacy Scale (CRTSE) and the Culturally Response Teaching Outcome Expectancy (CRTOE) Scale. Results suggest that middle school mathematics teachers were only moderately efficacious in their ability to implement culturally responsive teaching practices, despite strong beliefs in the instructional utility of culturally responsive teaching practices.

Cross Faculty Collaboration In The Development Of An Integrated Mathematics And Science Initial Teacher Education Program, Sharon P. Fraser, Kim Beswick, Margaret Penson, Andrew Seen, Robert Whannell

Australian Journal of Teacher Education

This paper describes a collaborative project involving mathematicians, scientists and educators at an Australian university where an innovative initial teacher education (ITE) degree in mathematics/science was developed. The theoretical frameworks of identity theory and academic brokerage and their use in understanding the challenges associated with the early stages of collaborative projects is described. Data from reflections and interviews of the participants after involvement in the project from one to three years are presented to illustrate these challenges. The paper concludes with a description of the importance of the academic broker in overcoming identity challenges and facilitating cultural change for academics …

Pre-Service Teachers’ Emerging Views On Educational Equity, Melody Wilson

Master's Theses and Doctoral Dissertations

An equity-based Statistics course for pre-service mathematics teachers could play a role in the development of pre-service teachers’ equity literacy, encouraging conversations about equity in education and illuminating structural factors that contribute to the educational opportunity gap in the U.S. In the Winter 2019 semester, a faculty team at the author’s university piloted such a course. The course included data explorations dealing with structural inequities by race – one of the most difficult topics to address productively in a teacher preparation course. For the present study, a survey of pre-service teachers’ views on educational equity was administered in a required …

What, How, Who: Developing Mathematical Discourse, Kelley E. Buchheister, Christa Jackson, Cynthia E. Taylor

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

A collaborative classroom, an open-ended problem, and a what-how-who structure can build students’ reasoning skills and allow teachers to recognize all classroom contributions.

With an increased focus on using social discourse to enhance students’ mathematical thinking and reasoning (NCTM 2014, Staples and King 2017), teachers are looking for discussion strategies that encourage middlelevel students to make sense of mathematical concepts. However, structuring these valuable discussions is complex. “Mathematical discourse should build on and honor student thinking, and provide students with opportunities to share ideas, clarify understandings, develop convincing arguments, and advance the mathematical learning of the entire class” (Smith, Steele, …

On "Icky" Data, The Political Classroom, And Towards Equity And Social Justice In Mathematics Education: A Conversation With Tonya Bartell, Samuel L. Tunstall, Oyemolade Osibodu, Tonya Gau Bartell

Numeracy

Tonya G. Bartell, ed. 2018. Towards Equity and Social Justice in Mathematics Education (Switzerland: Springer International Publishing) 341 pp. ISBN 978-3319929064.

This brief interview with Tonya Bartell introduces Towards Equity and Social Justice in Mathematics Education to the Numeracy audience. The interviewers also discuss with Tonya connections between quantitative literacy and mathematics for social justice, particularly in the context of US K-12 schooling. Tonya shares her perspective on topics ranging from the placement of quantitative literacy in K-12 mathematics education and how one might get started in incorporating a social justice lens into their teaching to paradigms for research …

Review Of Towards Equity And Justice In Mathematics Education, Edited By Tonya Gau Bartell, Emily Lardner

Numeracy

Tonya Grau Bartell, editor. 2018.Toward Equity and Social Justice in Mathematics Education. (Cham, Switzerland: Springer International Publishing). 341 pp. ISBN 978-3-319-92906-4 (also available as an e-book).

Toward Equity and Social Justice in Mathematics Education is a welcome addition to ongoing conversations about what mathematics should be taught and how it should be taught at both the college and pre-college level. Although the primary audience for the volume will be math educators and researchers, readers of this journal will discover intersecting interests, concerns, and strategies.

Elementary Teachers' Definitions And Usage Of Inquiry-Based Mathematics Instruction, Heather Nunnally

Theses and Dissertations

Current educational leaders call for students to build his or her own mathematical understanding from experiences, coupled with feedback from peers, teachers, and themselves and gain a conceptual understanding of mathematics. Researchers agree that inquiry in the elementary mathematics classroom can help increase conceptual understanding.

This case study focused on how elementary teachers define inquiry-based mathematics and implement it in their classrooms. Interviews, observations and lesson analysis were used to investigate what identities, relationships and activities look like in an elementary classroom that uses inquiry.

All of the participants felt "problem solving" and "working collaboratively" were essential for inquiry but …

Rural Teachers' Perceptions Of Collaboration And Professional Growth In Mathematics, Katherine M. Burns

University of the Pacific Theses and Dissertations

Teachers are a focal point in rural communities, building educational and cultural connections between the families and schools they serve on a daily basis. At the same time, geography and other constraints can impact rural teachers’ access to professional development and other resources. This mixed methods exploratory study focuses on a two-year professional learning program that supported rural teachers’ (n=38) professional growth in mathematics and encouraged the development of a collaborative Community of Practice spanning 14 elementary school sites in four Northern California counties.

Research methods incorporated a secondary data analysis, as well as the collection of new data. Quantitative …