Secondary Education and Teaching Commons^™

Using Sports To Develop Community In The Mathematics Classroom, Benjamin Lawson

Honors Projects

A positive classroom climate and community should be achieved in every classroom (Frisby, 2020, pgs. 199-200). This sense of community is especially sparse in the field of mathematics education. According to the High School Athletics Participation Survey (2019) the number of high schoolers participating in sports continues to rise. Sport ideologies could offer a bridge to connect mathematics classrooms and establish community in ways a pure educational perspective has not been able to. The purpose of this analysis is to shed light on an alternate perspective of mathematics education and incorporate sport philosophies to foster community building by establishing rapport, …

Investigating The Different Dimensions Of Preservice Mathematics Teachers’ Understanding – The Case Of Factorisation, Olivia Fitzmaurice, Jacqueline Hayes

Australian Journal of Teacher Education

This paper reports on a study designed to investigate preservice teachers’ understanding of factorisation, a topic not explicitly taught within their teacher education programme, but one they will be required to teach when they graduate. We query if the knowledge they bring from secondary school, prepares them sufficiently to teach their future students for understanding. 83 preservice secondary school mathematics teachers’ procedural and conceptual understanding of quadratic factorisation were assessed using Usiskin’s Framework for understanding mathematics (2012) which identifies several dimensions of understanding. The study provides evidence that the preservice mathematics teachers have a strong procedural understanding, and while some …

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 …

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 …

"Returning To The Root" Of The Problem: Improving The Social Condition Of African Americans Through Science And Mathematics Education, Vanessa R. Pitts Bannister, Julius Davis, Jomo Mutegi, Latasha Thompson, Deborah Lewis

Catalyst: A Social Justice Forum

The underachievement and underrepresentation of African Americans in STEM (Science, Technology, Engineering and Mathematics) disciplines have been well documented. Efforts to improve the STEM education of African Americans continue to focus on relationships between teaching and learning and factors such as culture, race, power, class, learning preferences, cultural styles and language. Although this body of literature is deemed valuable, it fails to help STEM teacher educators and teachers critically assess other important factors such as pedagogy and curriculum. In this article, the authors argue that both pedagogy and curriculum should be centered on the social condition of African Americans – …

The Role Of Sequence In The Experience Of Mathematical Beauty, Leslie Dietiker

Journal of Humanistic Mathematics

In this article, I analyze the aesthetic dimensions of a sequence of mathematical events found in an unusual first grade lesson in order to demonstrate how sequencing may affect an individual’s experience of mathematical beauty. By approaching aesthetic as a sense or felt quality of an experience in context (Sinclair, 2001, 2011), this analysis explains how sequence can affect the way mathematical objects or actions are experienced by an individual. Thus, rather than questioning whether or in what ways a set of mathematical objects are beautiful or not, this paper addresses under what conditions is the mathematics in play beautiful. …

Implementing Common Core State Standards For Mathematics Through Lesson Study, John Thomas Hall

Honors Program Projects

The Common Core State Standards for Mathematics (CCSSM) represent the beginning of a new era in American education. For the first time, a majority of states are sharing expectations for student knowledge in mathematics. While standards cannot change education, the means by which these standards are implemented contribute to the mathematical achievement of students. For instance, the CCSSM incorporate separate content and practice standards for students. Content standards are familiar to most educators, but the expectation of developing mathematical skills highlighted in the practice standards will require changes to lesson preparation and teaching.

In an effort to provide pre-service and …

What Is So Negative About Negative Exponents?, Geoffrey D. Dietz

Journal of Humanistic Mathematics

While teaching college-level mathematics (from College Algebra to Calculus to Abstract Algebra), I have observed that students are often uncomfortable using negative exponents in calculations. I believe the fault partially lies in the manner in which negative exponents are taught in Algebra 1 or Algebra 2 courses, especially in rigid instructions always to write answers using only positive exponents. After reviewing a sample of algebra texts used in the United States over the last two centuries, it appears that while attitudes toward negative exponents have varied from author to author over time, the current trend is to declare explicitly that …

Assessing U.S. High School Mathematics Students' Dependency On Calculators For Basic Arithmetic Operations Involving Integers From Single-Digit Fact Families, John Jeremy Sneed

Open Access Theses & Dissertations

This study was designed to investigate the extent to which high school students use calculators to perform basic operations, and how well they actually perform those same operations without using calculators. The investigation involved the testing of math classes of students--male and female, mixed ethnicities--in grades nine through twelve. Students were asked to perform all four basic math operations (add, subtract, multiply, divide) involving integers based on single-digit addition and multiplication fact families with and without calculators. The testing was in two environments--timed and untimed, with students recording their completion times--in order to investigate discrepancies in students' calculator use in …

A Primer For Mathematical Modeling, Marla A. Sole

Publications and Research

With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school with the mathematics they will use outside of school. Instructors have found mathematical modeling difficult to teach. To successfully incorporate modeling activities I believe that curricular changes should be accompanied by professional development for curriculum developers, classroom teachers, and higher education professionals. This article serves as an introduction to modeling by …

Teaching Mathematics For Social Justice: Conversations With Educators – A Symposium, David W. Stinson, Anita A. Wager

Middle-Secondary Education and Instructional Technology Faculty Publications

Using Marilyn Frankenstein’s germinal 1983 article “Critical Mathematics Education: An Application of Paulo Freire’s Epistemology” and Ole Skovsmose’s 1985 germinal article “Mathematics Education Versus Critical Education” as credible “start points”, critical mathematics or more broadly, social justice mathematics, is marking three decades of empowering yet uncertain possibilities. Nonetheless, there are two recurring questions: What is it? and What does it “look like”? Drawing on the collective stories (and wisdom) of critical mathematics educators, this symposium aims to offer some open, non-definitive answers to these two questions.

Conversations About Privilege And Oppression In Mathematics Education, David W. Stinson, Joi A. Spencer

Middle-Secondary Education and Instructional Technology Faculty Publications

In this editorial, the authors frame the purpose and outline the contents of the JUME special issue “Privilege and Oppression in the Mathematics Preparation of Teacher Educators” (the title of a 3-day conference held in Battle Creek, Michigan). As part of the “thoughtful action” called for throughout the conference, the intention of the special issue is to invite all mathematics educators (and others) into conversations about systems of privilege and oppression.

The Teaching And Learning Of Word Problems In Beginning Algebra : A Nigerian (Lagos State) Study, Omolola A. Ladele

Theses: Doctorates and Masters

At both the junior and senior secondary school levels in Nigeria, student performance in mathematics examinations has been poor. Within the context of large classes, with inadequate facilities, and teaching and learning in a second language, algebra and algebra word problems are introduced to students during their first year of junior secondary school. The transition from primary school arithmetic to the use of the algebraic letter is challenging to students and it is important that teachers should know the likely difficulties and misconceptions students may have as they begin algebra (Welder, 2012).

In this study, the impact of a teacher …

The Use Of Applets For Developing Understanding In Mathematics: A Case Study Using Maplets For Calculus With Continuity Concepts., Raymond Ellis Patenaude

Theses and Dissertations

The Common Core State Standards for Mathematics (CCSSM) are founded on a long history of mathematics education research emphasizing the importance of teaching mathematics for understanding. The CCSSM along with the National Council of Teachers of Mathematics (NCTM) recommend the use of technology in the teaching of mathematics. New mobile technologies in society facilitate use in mathematics classrooms, and these technologies rely on software applications called applets. Certain applets have been developed for use in teaching mathematics.

This study investigated the questions: Is it possible to determine the characteristics of applets that lead students toward greater understanding of mathematical concepts? …

Improving Pre-Service Teachers’ Adaptive Metacognitive Practices Through Reflective Writing, Joanne E. Goodell

Joanne E Goodell

In this study, the use of critical incident reflective writing as a means to engage pre-service secondary mathematics teachers in adaptive metacognitive practices is discussed. This basic interpretive qualitative study uses a sample of 5 incident reports from each of 37 students whose final papers were previously analyzed (for possible total of 185 incident reports). The qualitative data analysis software N-Vivo was used to code each incident using a broad initial set of codes which present evidence of teachers’ personal practical theories (PPTs), a vision of teaching that they would like to see enacted in their classroom, a sense of …

Addressing Impulsive Disposition: Using Non-Proportional Problems To Overcome Overgeneralization Of Proportionality, Kien Lim, Osvaldo Morera

Kien H Lim

Impulsive disposition is an undesirable way of thinking where one spontaneously applies the first idea that comes to mind without checking its relevance. In this research, we explore (a) the possibility of helping pre-service teachers improve their disposition, from being impulsive to being analytic, in one semester, and (b) the effect of using non-proportional situations. This study involves two sections of a mathematics course for pre-service teachers for Grades 4-8. The lessons were designed whenever possible to elicit students’ impulsive disposition so that they could become cognizant of it and make conscious attempts to overcome it. Some test items were …

Teachers Reflecting Differently: Deconstructing The Discursive Teacher/Student Binary, David W. Stinson, Ginny C. Powell

Middle-Secondary Education and Instructional Technology Faculty Publications

This session explores the ways that practicing teachers came to reflect differently regarding the discursive teacher/student binary during a graduate-level course entitled “Mathematics Education within the Postmodern.” Using Dewey’s concept of reflective thinking, as well as Foucault’s discourse and Derrida’s deconstruction, we show how the course provided new suggestions for the students as they continued their journey of becoming teachers. Through interweaving comments written by the students with concepts borrowed from postmodern philosophers and theorists, we illustrate how the teachers began to understand that teachers and students might indeed be described differently in the postmodern.

Becoming Critical Mathematics Pedagogues: A Journey, David W. Stinson, Carla R. Bidwell, Ginny C. Powell, Mary M. Thurman

Middle-Secondary Education and Instructional Technology Faculty Publications

This session will report the findings of a study that explored the beginning transformations in the pedagogical philosophies and practices of three mathematics teachers (middle, high school, and 2-year college) who completed a graduate-level mathematics education course that focused on critical theory and teaching for social justice, and how these transformations are compatible (or not) with reform mathematics education as suggested by the National Council of Teachers of Mathematics (NCTM), and in turn, the new Georgia Performance Standards (GPS). The study employed Freirian participatory research methodology; in fact, the participants were not only coresearchers, but also co-authors of the study. …

Critical Mathematics Pedagogy: Transforming Teachers’ Practices, David W. Stinson, Carla R. Bidwell, Christopher C. Jett, Ginny C. Powell, Mary M. Thurman

Middle-Secondary Education and Instructional Technology Faculty Publications

This study reports the effects of a graduate-level mathematics education course that focused on critical theory and teaching for social justice on the pedagogical philosophies and practices of three mathematics teachers (middle, high school, and 2-year college). The study employed Freirian participatory research methodology; in fact, the participants were not only co-researchers, but also co-authors of the study. Data collection included reflective essays, journals, and “storytelling”; data analysis was a combination of textual analysis and autoethnography. The findings report that the teachers believed that the course provided not only a new language but also a legitimization to transform their pedagogical …

What Is Mathematics?: Teachers Exploring The Philosophy Of Mathematics, Kimberly White-Fredette, David W. Stinson

Middle-Secondary Education and Instructional Technology Faculty Publications

No abstract provided.

Journaling As A Test Preparatory Measure In Secondary Mathematics: Successful Student Strategies, Lloyd E. Nickerson Ii

Master of Education Research Theses

This study examines a math journal writing assignment comparing how high school (grades 10 through 12) algebra students who performed well and students who performed poorly on traditional mathematics tests constructed their corresponding journal entries. Statistically significant differences found indicated that students who performed well on the tests were more likely to have originally composed the text and examples in their journal entries, and students who performed poorly were more likely to have copied much of the mathematical language and examples in their journal entries from their textbooks. Students who performed well on the test were also more likely to …

Using Critical Incident Reflections: A Self-Study As A Mathematics Teacher Educator, Joanne E. Goodell

Joanne E Goodell

In this paper, I report the results of a 4-year study into how my students learn to become mathematics teachers during the combined 15-week methods and field placement course I teach. At the start of most weekly methods class meetings, groups of three or four students reported their critical incidents to each other, and then chose one incident to report to the whole class. Each student then submitted a written report of 10 critical incidents for grading. At the end of each semester, I administered a questionnaire about the usefulness of each of the elements of the course. Using these …

Mathematics As “Gate-Keeper” (?): Three Theoretical Perspectives That Aim Toward Empowering All Children With A Key To The Gate, David W. Stinson

Middle-Secondary Education and Instructional Technology Faculty Publications

In this article, the author’s intent is to begin a conversation centered on the question: How might mathematics educators ensure that gatekeeping mathematics becomes an inclusive instrument for empowerment rather than an exclusive instrument for stratification? In the first part of the discussion, the author provides a historical perspective of the concept of “gatekeeper” in mathematics education. After substantiating mathematics as a gatekeeper, the author proceeds to provide a definition of empowering mathematics within a Freirian frame, and describes three theoretical perspectives of mathematics education that aim toward empowering all children with a key to the gate: the situated perspective, …

The Northeast Ohio Model Schools Project: A Pathway To Scaling Up Reform In Mathematics And Science, Joanne E. Goodell, Francis S. Broadway, Linda Gojak

Joanne E Goodell

The Northeast Ohio Model Schools Institute (NOMSI) provided professional development for school-based leadership teams in standards-based mathematics and science teaching practices and leadership skills. Leadership teams from six local school districts were recruited to attend a two-week summer institute in August 2001, which focused on national standards, principles of effective professional development, an understanding of the conditions necessary for change. One or two faculty from the College of Arts and Sciences at each university also participated in the summer institute. Teams prepared a professional development plan for their school or district and received a mini-grant to implement their plan. Coaches—experts …

The Northeast Ohio Model Schools Project: A Pathway To Scaling Up Reform In Mathematics And Science, Joanne E. Goodell, Francis S. Broadway, Linda Gojak

Francis Broadway

The Northeast Ohio Model Schools Institute (NOMSI) provided professional development for school-based leadership teams in standards-based mathematics and science teaching practices and leadership skills. Leadership teams from six local school districts were recruited to attend a two-week summer institute in August 2001, which focused on national standards, principles of effective professional development, an understanding of the conditions necessary for change. One or two faculty from the College of Arts and Sciences at each university also participated in the summer institute. Teams prepared a professional development plan for their school or district and received a mini-grant to implement their plan. Coaches—experts …

Assessing The Impact Of Sustained Professional Development On Middle School Mathematics Teachers, Joanne E. Goodell, Lesley H. Parker, Jane Butler Kahle

Joanne E Goodell

The study reported in this paper examines the impact of the Ohio Statewide Systemic Initiative (SSI) on participating mathematics teachers. Quantitative data from 90 SSI-trained teachers and 400 teachers without training, along with qualitative data collected from seven SSI teachers who were visited in their classrooms are presented. Analysis of the quantitative data showed that SSI and Non-SSI teachers reported significantly different frequencies of reformed teaching practices and held significantly different views about the nature and pedagogy of mathematics. Qualitative data from the interviews highlighted that the SSI professional development experience, the ability to find creative ways to overcome lack …