Education Commons^™

Teaching Undergraduates How To Analyze, Ryan Andrew Nivens, Rosalind Raymond Gann

Ryan Andrew Nivens

Analysis is typically the first of the higher functions listed in taxonomies of higher order thinking. Academics consider these upper categories extremely worthwhile, but they are hard to teach and we are apt to ignore them. Today higher education is being criticized for “dumbing down” curriculum or lowering standards. To rectify this, many policies at the state or national level are requiring higher education institutions to change. In K‐12 education, Race to the Top and Common Core requirements are placing new demands on K‐12 teacher preparation, which include evaluation of the analysis skills of pre‐service teachers. But professors do not …

English Language Learners In The Mathematics Classroom, Julia Mccormick

Senior Honors Projects

Mathematics is often considered a universal language. Most of us have heard this statement from a math teacher at some point throughout our academic careers. However, for students moving to the United States from another country with minimal fluency in English, this is clearly not the case. They may walk into math class, a subject area in which they may have excelled in their native country, and see the words “polynomial”, “coefficient”, and “differentiate” on the board. Regardless of their experiences in their native language, there are disconnects and cultural differences between languages and skills emphasized that prevents mathematics from …

"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 – …

Impact Of Kinesthetic Learning On Student Knowledge Retention And Attitudes Toward Mathematics, Alyssa Lustgarten

Honors Projects

This research study examines the impact of kinesthetic learning on student knowledge retention and attitudes toward mathematics. Specifically, this study focuses on teaching mathematics to secondary students through dance. Quantitative data was collected and analyzed regarding student mathematics knowledge retention and student attitudes towards mathematics. Although student mathematics knowledge retention increased for both the control and treatment groups, student attitudes toward mathematics decreased after the intervention for the treatment group.

What’S Brewing? A Statistics Education Discovery Project, Marla A. Sole, Sharon L. Weinberg

Publications and Research

We believe that students learn best, are actively engaged, and are genuinely interested when working on real-world problems. This can be done by giving students the opportunity to work collaboratively on projects that investigate authentic, familiar problems. This article shares one such project that was used in an introductory statistics course. We describe the steps taken to investigate why customers are charged more for iced coffee than hot coffee, which included collecting data and using descriptive and inferential statistical analysis. Interspersed throughout the article, we describe strategies that can help teachers implement the project and scaffold material to assist students …

Math Is More Than Numbers: Beginning Bilingual Teachers’ Mathematics Teaching Practices And Their Opportunities To Learn, Cathery Yeh

Education Faculty Articles and Research

In this article, the author provides results from a 3-year, longitudinal study that examined two novice bilingual teachers’ mathematics teaching practices and their professional opportunities to learn to teach. Primary data sources included videotaped mathematics lessons, teacher interviews, and field notes of their teacher preparation methods courses. Findings revealed that the teachers were oriented toward differing views of learning that shaped how they organized students’ learning of language and mathematics during classroom instruction. While both teachers used similar teaching strategies to support students’ development of mathematics specific literacies, there were variances in how the learners were positioned within the classroom …

Increasing Engagement Of Students With Learning Disabilities In Mathematical Problem-Solving And Discussion, Rachel Lambert, Trisha Sugita

Education Faculty Articles and Research

Engagement in problem-solving and mathematical discussion is critical for learning mathematics. This research review describes a gap in the literature surrounding engagement of students with Learning Disabilities in standards-based mathematical classrooms. Taking a sociocultural view of engagement as participation in mathematical practices, this review found that students with LD were supported towards equal engagement in standards-based mathematics through multi-modal curriculum, consistent routines for problem-solving, and teachers trained in Mathematical Knowledge for Teaching. Using this small set of studies (7), we identify the need to deepen the engagement of students with LD in mathematical problem-solving and discussion. This review concludes with …

Working Together: A Caring Relation Between A Teacher And A Mathematics Educator, Elizabeth Suazo Flores

Purdue Journal of Service-Learning and International Engagement

Using Noddings’s (1984) caring theory, Elizabeth Suazo Flores—a third-year PhD student in mathematics education—describes how a caring relationship developed between her and an eighth grade mathematics teacher, Lisa. Noddings’s (1984) caring theory provided insights into their community-based experience, which was characterized by trust and open-mindedness.

Online Mathematics Homework Increases Student Achievement, Jeremy Roschelle, Mingyu Feng, Robert F. Murphy, Craig A. Mason

STEM Faculty Scholarship

In a randomized field trial with 2,850 seventh-grade mathematics students, we evaluated whether an educational technology intervention increased mathematics learning. Assigning homework is common yet sometimes controversial. Building on prior research on formative assessment and adaptive teaching, we predicted that combining an online homework tool with teacher training could increase learning. The online tool ASSISTments (a) provides timely feedback and hints to students as they do homework and (b) gives teachers timely, organized information about students’ work. To test this prediction, we analyzed data from 43 schools that participated in a random assignment experiment in Maine, a state that provides …

Effects Of Guided Project-Based Learning Activities On Students’ Attitudes Toward Statistics In An Introductory Statistics Course, Timothy Jonathan Bayer

STEMPS Theses & Dissertations

This research sought to determine if the use of a guided project-based learning instructional approach improved students’ attitudes and academic performance in a college-level introductory statistics course at a community college. It also sought to determine if the guided project-based approach improved attitudes and academic performance more than a traditional lecture-based instructional approach. The research used a quasi-experimental Pre-test, Post-test approach. The independent variable was either the use of a guided project-based learning instructional approach or the use of a traditional lecture-based instructional approach. The dependent variables were student attitudes and final course grades. Students’ attitudes were measured using the …

Teacher Self-Perceptions And Student Academic Engagement In Elementary School Mathematics., Kathleen M. Cash

Electronic Theses and Dissertations

This study examined the relationship between elementary students’ academic engagement in mathematics and their teachers’ self-perceptions in mathematics. Early success in mathematics is seen as crucial for later success academically and professionally. Framed in Social Cognitive Theory this study sought to build on past research studies, which have found that student affective characteristics such as academic engagement, comprised of both behavioral and emotional engagement, vary across genders and ability levels. This study sought to use a number of control and independent variables to examine academic engagement in students and the relationship of that engagement to teachers’ mathematics self-concept and teaching …

Social Justice And Writing In A Math Classroom, Jesica Chaya

Honors Senior Capstone Projects

By intertwining new math concepts with important and relevant social issues, teachers can empower students to recognize the applicable nature of math to problems that their generation will be dealing with for years to come. In doing this, they can also change students’ perceptions of what succeeding in a math class looks like and address a rising necessity for writing across the curriculum by connecting these social justice based plans with writing assignments that encourage and reinforce vocabulary and a deep understanding of the material.

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. …

Journal Rankings And Representation In Mathematics Education, Samuel Otten, Ryan Andrew Nivens

ETSU Faculty Works

Excerpt: Publish or perish has long been the mantra academics live by. For decades, this referred to a list of publications on a researcher’s Curriculum Vitae.

Dewey, Freire, And Foucault And An Ever-Evolving Philosophy Of (Mathematics) Education, David W. Stinson

Middle and Secondary Education Faculty Publications

In this essay, the author provides a working definition of philosophy from a cultural point of view, and argues the need for mathematics educators to develop their philosophy of mathematics teaching and learning or, to speak more broadly, their philosophy of education. He then historically situates three scholars—John Dewey, Paulo Freire, and Michel Foucault—who have been instrumental in the formulation of his philosophy of education. Next, he shares how the philosophies of these three scholars provide different languages to critique three aspects of education. He concludes with brief discussions on the process of his ever-evolving philosophy of mathematics teaching and …

Mathematics For What? High School Students Reflect On Mathematics As A Tool For Social Inquiry, Anastasia Brelias

Democracy and Education

This study examines high school students’ views of mathematics as a tool for social inquiry in light of their classroom experiences using mathematics to explore social issues. A critical theoretical perspective on mathematics literacy is used to ascertain the ways in which their views challenge or affirm the dominant image of mathematics in society. The study concludes that mathematics applications addressing social justice issues are promising vehicles for developing students’ appreciation of mathematics as a social problem-solving tool, an awareness of its limitations, and a healthy skepticism toward its uses.

Integrating Math And Literature In The Elementary Classroom, Megan Maureen Boebinger

Undergraduate Honors Thesis Collection

Growing up, I was the student who hated to go to math class. I was not bad at math, I just could not seem to find a way to make it interesting or exciting. I had trouble understanding the purpose of math and how it was applicable to my own life. Word problems were my worst enemy; I appreciated the attempt to make math seem relatable, but never saw the use. Many of these problems involved building or buying something; topics I had no experience with in elementary school. I did not see why I needed to know the exact …

Improving Number Sense Using Number Talks, Kelsie Ruter

Master of Education Program Theses

This action research study examines the effects of using number talks instruction in the second grade classroom on number sense/critical thinking in mathematics. The sample included 47 students from two second grade classes in two suburban public elementary schools serving mostly upper middle class neighborhoods. For four weeks in the middle of the second trimester, an experimental group was exposed to the teaching of math through number talks, in addition to their regular math instruction. A control group was instructed using their regular methods and curriculum. Both groups were given a pretest and posttest of “rich math tasks.” Comparison data …

Parting Thoughts - So Much More To Discover, Eric L. Mann

Faculty Publications

No abstract provided.

A Method For Assessing And Describing The Informal Inferential Reasoning Of Middle School Students, Joshua Michael Goss

Dissertations

Informal Inferential Reasoning (IIR) has emerged in the last decade in the study of statistics education. Developing students’ IIR ability is seen as a way of preparing students for the important topic of Formal Statistical Inference (FSI); however, research is still needed in order to investigate how students transition between informal and formal statistical reasoning. A primary difficulty is that we do not have a way of assessing and describing students’ IIR ability levels. In order to address this, an Assessment of Informal Inferential Reasoning (AIIR) was developed, along with a Structure of Observed Learning Outcomes (SOLO) taxonomy (Biggs & …

Supporting Student Justification In Middle School Mathematics Classrooms: Teachers' Work To Create A Context For Justificaiton, Megan Staples

CRME Publications

Justification is an important disciplinary and learning practice. Despite a growing knowledge base regarding how teachers orchestrate mathematical discussions, few analyses have considered the orchestration of specific disciplinary practices such as justification. Using classroom video data from the JAGUAR project, we analyze two instantiations of extensive student justification in seventh-grade classrooms and document each teacher’s pedagogical approach that supported students’ engagement in this practice. We argue that, although there was overlap in their pedagogical repertoires, the teachers created a context for student justification in two unique ways. We document the similarities and differences in their approaches, including the nature of …

Mastery Learning In Calculus I Affects Student Learning, Grade Improvement, And Professor Exhaustion, Judith Puncochar, Don H. Faust

Conference Presentations

Three Calculus I courses were taught under conditions of either traditional teaching, 2/3 mastery, or full mastery to test four hypotheses. Under conditions of mastery learning on exams, students should attain appropriate higher-level mathematical concepts, achieve more learning of higher-level mathematical concepts, learn higher-level mathematical concepts more quickly, and evaluate mastery learning favorably. Support for all hypotheses occurred only in the 2/3 mastery condition. A shift toward higher grades was attributed to grade improvement, not grade inflation, as determined by six mathematicians with blind review of final exam items. Final exams in mastery learning courses were significantly more …

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 …

The Adoption Of Open Educational Resources By One Community College Math Department, John Hilton Iii, Donna Gaudet, Phil Clark, Jared Robinson, David Wiley

Faculty Publications

The high cost of textbooks is of concern not only to college students but also to society as a whole. Open textbooks promise the same educational benefits as traditional textbooks; however, their efficacy remains largely untested. We report on one community college’s adoption of a collection of open resources across five different mathematics classes. During the 2012 fall semester, 2,043 students in five different courses used these open access resources. We present a comparison between the previous two years in terms of the number of students who withdrew from the courses and the number that completed the courses with a …

Teaching Undergraduates How To Analyze, Ryan Andrew Nivens, Rosalind Raymond Gann

ETSU Faculty Works

Analysis is typically the first of the higher functions listed in taxonomies of higher order thinking. Academics consider these upper categories extremely worthwhile, but they are hard to teach and we are apt to ignore them. Today higher education is being criticized for “dumbing down” curriculum or lowering standards. To rectify this, many policies at the state or national level are requiring higher education institutions to change. In K‐12 education, Race to the Top and Common Core requirements are placing new demands on K‐12 teacher preparation, which include evaluation of the analysis skills of pre‐service teachers. But professors do not …

Parts Of The Whole: When Variation Is The Goal, Dorothy Wallace

Numeracy

The goals of higher education are a population of extreme variability in expertise, a diffusion of specialized knowledge across disciplinary boundaries, and production of strong K-12 teachers. Promoting these three goals has implications at all granularities, from the pedagogy of an individual college professor to the incentives and policies that shape systemic change.

Online Resources Platform For Mathematics Education, Marisa Llorens, Edmund Nevin, Eileen R. Mageean

Other resources

The aim of this project was to develop and explore the use of a Sharable Content Object Reference Model (SCORM) integrating a web-based platform for the study of mathematics as part of an active learning environment. The platform was designed to provide active support to engineering students especially those in their first year of study. Early use of the platform can identify possible areas of weakness and provide the self-learning environment required for students to become more proficient in areas where they are lacking key skills or are finding the concepts difficult to understand. The platform consists of a set …

Conceptual Understanding Of Fractions And Decimals For Fourth Grade Students, Sarah J. Appleton

Boise State University Theses and Dissertations

A study was conducted in two 4th grade classrooms based on current research of foundational concepts of fraction and decimal knowledge, socio-cultural learning theory, cognition and international mathematics education. The goal of this study was for students to acquire conceptual and procedural knowledge of fraction and decimal concepts. When students have multiple experiences delving into rigorous tasks with fractions and decimals, researchers (Lamon, 2006; Siegler & Alibali 2005) suggest students will show an increase in understanding. Cognition and developmental stages were examined and incorporated within the suggested tasks of the instructional unit. With assistance from current research, this study demonstrated …

Implementing A Blended Model Of Mathematics Instruction – Issues And Outcomes, Natasha Brewley, Alvina Atkinson, Barry Biddlecomb

SoTL Commons Conference

The session will present issues and results from the implementation of a blended instruction model at the authors' institution. The blended instruction model involves coming together as a class less often and encourages student learning by making them more responsible for their learning outside of the classroom. In addition to describing the authors' home institution, this presentation will have three objectives: (1) Describe the blended instructional model (What is Blended learning and what does it look like?), (2) Present student evaluations. (What have students said about taking a course like this?), and (3) Present quantitative comparisons between blended and traditional …

Preservice Secondary School Mathematics Teachers' Current Notions Of Proof In Euclidean Geometry, Michael Ratliff

Doctoral Dissertations

Much research has been conducted in the past 25 years related to the teaching and learning of proof in Euclidean geometry. However, very little research has been done focused on preservice secondary school mathematics teachers’ notions of proof in Euclidean geometry. Thus, this qualitative study was exploratory in nature, consisting of four case studies focused on identifying preservice secondary school mathematics teachers’ current notions of proof in Euclidean geometry, a starting point for improving the teaching and learning of proof in Euclidean geometry.

The unit of analysis (i.e., participant) in each case study was a preservice mathematics teacher. The case …