Education Commons^™

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.

An Extensible Technology Framework For Cyber Security Education, Frank Jordan Sheen

Theses and Dissertations

Cyber security education has evolved over the last decade to include new methods of teaching and technology to prepare students. Instructors in this field of study often deal with a subject matter that has rigid principles, but changing ways of applying those principles. This makes maintaining courses difficult. This case study explored the kind of teaching methods, technology, and means used to explain these concepts. This study shows that generally, cyber security courses require more time to keep up to date. It also evaluates one effort, the NxSecLab, on how it attempted to relieve the administrative issues in teaching these …

An African-Centered Approach To Land Education, Salvotore Engel-Dimauro, Karanja Keita Carroll

Publications and Research

Approaches to environmental education which are engaging with place and critical pedagogy have not yet broadly engaged with the African world and insights from Africana Studies and Geography. An African-centered approach facilitates people's reconnection to places and ecosystems in ways that do not reduce places to objects of conquest and things to be exploited for profitability and individual gain. Such an approach offers effective critiques of settler coloniser perspectives on the environment and deeper understandings of the relationship between worldview and ecologically sensitised education. Through examples from Africana Studies and Geography, this article provides an introduction to how an African-centered …

Why Rozenzweig-Style Midrashic Approach Makes Rational Sense: A Logical (Spinoza-Like) Explanation Of A Seemingly Non-Logical Approach, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

A 20 century German Jewish philosopher Franz Rosenzweig promoted a new approach to knowledge, an approach in which in addition to logical reasoning, coming up with stories with imagined additional details is also important. This approach is known as midrashic since it is similar to the use of similar stories -- known as midrashes -- in Judaism. While stories can make the material interesting, traditionally, such stories are not viewed as a serious part of scientific discovery. In this paper, we show that this seemingly non-logical approach can actually be explained in logical terms and thus, makes perfect rational sense.

Ipads In The Classroom Pilot Project, Anu Vedantham, Caitlin Shanley

Anu Vedantham

The Gaise College Report: The American Statistical Association Meets Sound Pedagogy In Central Virginia, Beverly Wood

Publications

Research in undergraduate statistics education often centers on the introductory course required for a large percentage of college students. While acknowledging the diverse setting, audience, and purpose of introductory courses, existing research assumes that courses offered by different disciplines share the same goals and teaching practices. The purpose of this study is to examine the objectives for student outcomes and pedagogical delivery of introductory statistics courses in various academic departments to provide explicit evidence for this assumption. The American Statistical Association’s Guidelines for Assessment and Instruction in Statistics Education (GAISE) are meant to apply to all introductory courses. The College …

A Multi-Platform Application Suite For Enhancing South Asian Language Pedagogy, Tao Bai, Christopher K. Chung, Konstantin Läufer, Daisy Rockwell, George K. Thiruvathukal

Konstantin Läufer

This interdisciplinary project explores the potential for handheld/wireless (H/W) technology in the context of language education within and beyond the classroom. Specifically, we have designed and implemented a suite of multi-platform (desktop/laptop, handheld, and browser) applications to enhance the teaching of South Asian languages such as Hindi-Urdu. Such languages are very difficult to learn, let alone write, and H/W devices (with their handwriting/drawing capabilities) can play a significant role in overcoming the learning curve. The initial application suite includes a character/word tracer, a word splitter/joiner, a smart flashcard with audio, contextual augmented stories for reading comprehension, and a poetic metronome. …

Parts Of The Whole: Learn More, Learn Better, Dorothy Wallace

Numeracy

Building on previous columns in Numeracy, this column analyzes various teaching techniques in terms of their ability to build cognitive schema, extend existing schema, reinforce learning, move mean understanding of a group of students, and reduce variance in understanding of a group. We offer a pedagogical cycle as an example of how to address multiple learning goals using common teaching methods.

A Multi-Platform Application Suite For Enhancing South Asian Language Pedagogy, Tao Bai, Christopher K. Chung, Konstantin Läufer, Daisy Rockwell, George K. Thiruvathukal

George K. Thiruvathukal

This interdisciplinary project explores the potential for handheld/wireless (H/W) technology in the context of language education within and beyond the classroom. Specifically, we have designed and implemented a suite of multi-platform (desktop/laptop, handheld, and browser) applications to enhance the teaching of South Asian languages such as Hindi-Urdu. Such languages are very difficult to learn, let alone write, and H/W devices (with their handwriting/drawing capabilities) can play a significant role in overcoming the learning curve. The initial application suite includes a character/word tracer, a word splitter/joiner, a smart flashcard with audio, contextual augmented stories for reading comprehension, and a poetic metronome. …

The Extreme Software Development Series: An Open Curricular Framework For Applied Capstone Courses, Konstantin Läufer, George K. Thiruvathukal

George K. Thiruvathukal

We describe an open, flexible curricular framework for offering a collection of advanced undergraduate and graduate courses in software development. The courses offered within this framework are further unified by combining solid foundations with current technology and play the role of capstone courses in a modern software development track. Our initiative has been very successful with all stakeholders involved.

A Study Analyzing Five Instructional Methods For Teaching Software To Junior High Students, Scott Ronald Bartholomew

Theses and Dissertations

If you ask 5 different teachers what the best way to teach a new technology to a student is you will get 5 different answers. (Bork, 2001; Cheong, 2008; Egal, 2009; Howell, 2001) What is the best way to teach a new computer software application to a student? In the technological world we live in today the effective transfer of technological knowledge is paramount. With varying opinions even among the leaders of national technology teacher associations (Haynie, 2005) there is a large level of ambiguity in relation to best practices in technology teaching. This study evaluates five commonly used methods …

What Do We Mean By Mathematical Proof?, Todd Cadwalladerolsker

Journal of Humanistic Mathematics

Mathematical proof lies at the foundations of mathematics, but there are several notions of what mathematical proof is, or might be. In fact, the idea of mathematical proof continues to evolve. In this article, I review the body of literature that argues that there are at least two widely held meanings of proof, and that the standards of proof are negotiated and agreed upon by the members of mathematical communities. The formal view of proof is contrasted with the view of proofs as arguments intended to convince a reader. These views are examined in the context of the various roles …

Mathematics In The Age Of Technology: There Is A Place For Technology In The Mathematics Classroom, Helen Crompton

Teaching & Learning Faculty Publications

In today’s world of ubiquitous computing there are a number of technologies available to K-12 educators for teaching and learning mathematics. However, Koehler and Mishra (2008) have described how teaching and learning with such technologies presents a “wicked problem,” as it can involve a number of variables, independent of each other and contextually bound, that need to be brought together. This article highlights the advantages technology offers for mathematics education and looks at some of the reasons behind the poor uptake, such as teacher beliefs and lack of training. A number of solutions are offered to address these issues, including …

Calculus, Biology And Medicine: A Case Study In Quantitative Literacy For Science Students, Kim Rheinlander, Dorothy Wallace

Numeracy

This paper describes a course designed to enhance the numeracy of biology and pre-medical students. The course introduces students with the background of one semester of calculus to systems of nonlinear ordinary differential equations as they appear in the mathematical biology literature. Evaluation of the course showed increased enjoyment and confidence in doing mathematics, and an increased appreciation of the utility of mathematics to science. Students who complete this course are better able to read the research literature in mathematical biology and carry out research problems of their own.

Spreadsheets Across The Curriculum, 1: The Idea And The Resource, H L Vacher, Emily Lardner

Numeracy

This paper introduces Spreadsheets Across the Curriculum, a workshop-based educational materials development project to build a resource to facilitate connecting mathematics and context in undergraduate college courses where mathematical problem solving is relevant. The central idea is “spreadsheet modules,” which, in essence, are elaborate word problems in the form of short PowerPoint presentations with embedded Excel spreadsheets. Students work through the presentations on their own, making and/or completing the spreadsheets displayed on the slides in order to perform calculations or draw graphs that address the issue (context) posed in the word problem. The end result of the project is the …

The Case For Infusing Quantitative Literacy Into Introductory Geoscience Courses, Jennifer M. Wenner, Eric M. Baer, Cathryn A. Manduca, R. Heather Macdonald, Samuel Patterson, Mary Savina

Numeracy

We present the case for introductory geoscience courses as model venues for increasing the quantitative literacy (QL) of large numbers of the college-educated population. The geosciences provide meaningful context for a number of fundamental mathematical concepts that are revisited several times in a single course. Using some best practices from the mathematics education community surrounding problem solving, calculus reform, pre-college mathematics and five geoscience/math workshops, geoscience and mathematics faculty have identified five pedagogical ideas to increase the QL of the students who populate introductory geoscience courses. These five ideas include techniques such as: place mathematical concepts in context, use multiple …

Addressing The Principles For School Mathematics: A Case Study Of Elementary Teachers Pedagogy And Practices In An Urban High-Poverty School, Robert Q. Berry, Linda Bol, Sueanne E. Mckinney

Educational Foundations & Leadership Faculty Publications

The extent to which four novice teachers assigned to an urban high-poverty school implemented the Principles of School Mathematics during their mathematics instruction program was investigated using a case study design. The research team conducted 36 unannounced observations of the participating teachers and utilized a developed assessment to guide their observations. Results indicated that only one teacher was judged proficient for all the principles. The remaining three teachers fell short in the implementation and direction of the principles. Detailed descriptions of the pedagogical practices of the teachers are provided.

Imagine Math Day: Encouraging Secondary School Students And Teachers To Engage In Authentic Mathematical Discovery, Darryl H. Yong, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

Research mathematicians and school children experience mathematics in profoundly different ways. Ask a group of mathematicians what it means to “do mathematics” and you are likely to get a myriad of responses: mathematics involves analyzing and organizing patterns and relationships, reasoning and drawing conclusions about the world, or creating languages and tools to describe and solve important problems. Students of mathematics often report “doing mathematics” as performing calculations or following rules. It’s natural that they see mathematics as monolithic rather than an evolving, growing, socially constructed body of knowledge, because most mathematical training in primary and secondary schools consists of …

The Art Of Teaching Mathematics, Garikai Campbell, Jon T. Jacobsen, Aimee S A Johnson, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

On June 10–12, 2007, Harvey Mudd College hosted A Conference on the Art of Teaching Mathematics. The conference brought together approximately thirty mathematicians from the Claremont Colleges, Denison, DePauw, Furman, Middlebury, Penn State, Swarthmore, and Vassar to explore the topic of teaching as an art. Assuming there is an element of artistic creativity in teaching mathematics, in what ways does it surface and what should we be doing to develop this creativity?

Teaching Time Savers: The Exam Practically Wrote Itself!, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

When I first started teaching, creating an exam for my upper division courses was a genuinely exciting process. The material felt fresh and relatively unexplored (at least by me), and I remember often feeling pleasantly overwhelmed with what seemed like a vast supply of intriguing and engrossing exam-ready problems. Crafting the perfect exam, one that was noticeably inviting, exceedingly fair, and unavoidably illuminating, was a real joy.

Teaching Time Savers: Is Homework Grading On Your Nerves?, Lisette G. De Pillis, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

You have probably heard it said that we learn mathematics best when we do mathematics, or that mathematics is not a spectator sport. For most of our students, this means that their mathematics courses will involve a fair amount of homework. This homework is often used to evaluate individual student progress, but it can also be used, for example, as a catalyst for discussion, to emphasize a point made in class, and to identify common misunderstandings throughout the class as a whole. There is, however, the matter of grading homework.

Teaching Time Savers: Some Advice On Giving Advice, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

There are always a lot of questions that need to be answered at the beginning of a course. When are office hours? What are the grading policies? How many exams will there be? Will late homework be accepted? We have all seen the answers to these sorts of questions form the bulk of a standard course syllabus, and most of us feel an obligation (and rightly so) to provide such information.

Teaching Time Savers: Style Points, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

When I began as an assistant professor, I had a pretty good sense of how much time it would take for me to prepare for each class. After a few conversations with my new colleagues, I even had a good sense of how much time I should devote to tasks like office hours and committee work. Somewhere in the middle of grading my first exam, though, it became painfully clear that I had underestimated the amount of time I would need to grade exams!

Teaching Time Savers: A Recommendation For Recommendations, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

I admit it — I enjoy writing recommendation letters for my students. I like
learning about their hopes and dreams, where they have been and where they want to go. A recommendation letter is an opportunity to remind myself how much my students can grow while they are in college, and how much I have grown as an instructor, advisor, and mentor.

Looking Beyond The Curriculum In Jamaica, Jon T. Jacobsen, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

In August 2004, we had the opportunity to travel to Jamaica to lead a pilot workshop for Jamaican high school math teachers. The workshop focused on the importance of mathematical context in the teaching of mathematics. It was sponsored by the Gibraltar Institute, a Jamaica-based nongovernmental organization led by Trevor Campbell (Pomona College) and Reginald Nugent (Cal State Pomona), Jamaica’s College of Agriculture, Science and Education, and Harvey Mudd College.

Teaching Statistics With Sports Examples, Paul Kvam, Joel Sokol

Department of Math & Statistics Faculty Publications

Class material for introductory and advanced statistics can be colorfully illustrated by using appropriate data and examples from sports. Specific methods, including statistical graphics (e.g., boxplots), ball-and-urn probabilities, and statistical regression are demonstrated. Examples are drawn from popular American sports such as baseball, basketball, soccer and American football. Classroom feedback indicates that most students enjoy sports examples as a way to learn abstract concepts using familiar, recreational settings.

A Multi-Platform Application Suite For Enhancing South Asian Language Pedagogy, Tao Bai, Christopher K. Chung, Konstantin Läufer, Daisy Rockwell, George K. Thiruvathukal

Computer Science: Faculty Publications and Other Works

This interdisciplinary project explores the potential for handheld/wireless (H/W) technology in the context of language education within and beyond the classroom. Specifically, we have designed and implemented a suite of multi-platform (desktop/laptop, handheld, and browser) applications to enhance the teaching of South Asian languages such as Hindi-Urdu. Such languages are very difficult to learn, let alone write, and H/W devices (with their handwriting/drawing capabilities) can play a significant role in overcoming the learning curve. The initial application suite includes a character/word tracer, a word splitter/joiner, a smart flashcard with audio, contextual augmented stories for reading comprehension, and a poetic metronome. …