Science and Mathematics Education Commons^™

Choose Your Words: Refining What Counts As Mathematical Discourse In Students' Negotiation Of Meaning For Rate Of Change Of Volume, Christine Johnson

Theses and Dissertations

The purpose of this study is to describe how university honors calculus students negotiate meaning and language for conceptually important ideas through mathematical discourse. Mathematical discourse has been recognized as an important topic by mathematics education researchers of various theoretical perspectives. This study is written from a perspective that merges symbolic interactionism (Blumer, 1969) with personal agency (Walter & Gerson, 2007) to assert that human choice reflects, but is not determined by, meanings that are primarily developed through social interaction. The process of negotiation of meaning is identified, described, and analyzed in the discourse of four students and their professor …

Parts Of The Whole: Teachers And The Work They Do, Dorothy Wallace

Numeracy

This introductory column argues the need to study our system of education with the same care we would give any complex system, pointing out some ways in which the educational system functions differently from other managed systems, and concluding that a careful study of the forces shaping education will lead to insight into what makes educational change successful.

Review Of Quantitative Reasoning: Tools For Today's Informed Citizen By A. Sevilla And K. Somers, Aaron G. Montgomery

Numeracy

Alicia Sevilla and Kay Somers, Quantitative Reasoning: Tools for Today’s Informed Citizen. (Emeryville CA: Key College Publishing, 2007). 626 pp. Softcover with Student CD. $79.95 (USA) ISBN 1-931914-90-1. http://www.keycollege.com/catalog/titles/quantitative_reasoning.html

From charts and graphs (Topic 1) to decision making (Topic 21), Quantitative Reasoning offers a good selection of topics that students in a general education mathematics course and other individuals in our society should understand. Organizing the 21 chapters (topics) under the headings of numerical reasoning, logical reasoning, and statistical reasoning, Sevilla and Somers focus their chapters on examples and devote the last 224 pages to 21 Excel activities. Parallel graphic-calculator …

Word Problems: Reflections On Embedding Quantitative Literacy In A Calculus Course, Gizem Karaali

Numeracy

Even though Quantitative Literacy (QL) programs are currently being developed and implemented in several colleges and universities, most schools still depend on traditional mathematics courses to reach their quantitative literacy goals. This note is a case study of how a traditional mathematics course sequence intended for students majoring in social and life sciences may be modified and adapted to at least partially fulfill the need in the absence of a stand-alone QL program. In particular, we focus on a freshman-level mathematics course sequence that serves various client departments. This sequence covers the traditional content of a first-year calculus sequence along …

False Positives And Referral Bias: Content For A Quantitative Literacy Course, Stuart Boersma, Teri Willard

Numeracy

An extended study of accuracy in medical screening is presented as a useful application to increase students’ quantitative reasoning skills. Two detailed examples are presented. The first explores the frequency of obtaining false positive results from a medical screening tool while the second examines the issue of referral bias and its effect on the apparent sensitivity and specificity of the screening tool. Results from student assessments indicate that the activity increases one’s ability to define terms such as “false positive” and “false negative” and increases one’s ability to read and compute with information obtained from a two-way table. Teacher assessment …

Using Local Data To Advance Quantitative Literacy, Stephen Sweet, Susanne Morgan, Danette Ifert Johnson

Numeracy

In this article we consider the application of local data as a means of advancing quantitative literacy. We illustrate the use of three different sources of local data: institutional data, Census data, and the National College Health Assessment survey. Our learning modules are applied in courses in sociology and communication, but the strategy of using local data can be integrated beyond these disciplinary boundaries. We demonstrate how these data can be used to stimulate student interests in class discussion, advance analytic skills, as well as develop capacities in written and verbal communication. We conclude by considering concerns that may influence …

Quantitative Literacy Across The Curriculum: A Case Study, Benjamin Steele, Semra Kiliç-Bahi

Numeracy

We describe a quantitative literacy (QL) program at Colby-Sawyer College, a small, residential, liberal arts college in New Hampshire. This program has grown rapidly from a traditional math curriculum to a college-wide understanding of quantitative literacy and voluntary participation by many faculty members in all departments. More than 80% of the faculty agreed that it would be useful for students to be able to use quantitative skills in their courses, but only 24 % thought students were capable of doing very well in mathematics. Twenty-three faculty members attended a summer workshop, funded by NSF, DUE # 0633133, in which they …

Quantitative Literacy On The Web Of Science, 1: The Bibliography And Its Role In The History Of This Journal, H L. Vacher, Todd Chavez

Numeracy

Prior to deciding to propose in 2006 that the National Numeracy Network (NNN) publish a new journal for quantitative literacy with their support, the University of South Florida Libraries investigated the publication environment of the field on the Web of Science®. Reproducing part of that study in this paper, we present findings from topic searches (March 2008) for “numeracy,” “quantitative literacy,” and “statistical literacy.” These updated results include a combined bibliography of 338 peer-reviewed articles amongst 210 different journals, by 748 authors from 321 institutions in 25 countries, in a total of 87 subjects (34% of the subject classes in …

Abstracts For Numeracy, H L. Vacher

Numeracy

No abstract provided.

Iowa Academy Of Science: The New Bulletin, V04n2, Summer 2008, Iowa Academy Of Science

New Bulletin

Inside This Issue:

--Message from the Executive Director

--REAP-CEP Funds Iowa Project WET

--Invitation to the 2008 Iowa Science Teachers’ Section Fall Conference

--Kaitlynn Hood Awarded ESTA for Elementary Science Education

--Scrapbook 2007-2008

Wythoff’S Game, Kimberly Hirschfeld-Cotton

Department of Mathematics: Master of Arts in Teaching, Exam Expository Papers

Wythoff’s Game, named after Willem Abraham Wythoff, is a well known game amongst number theorists. Dr. Wythoff, who received a Ph. D. in mathematics from the University of Amsterdam in 1898, described this game in these words: “The game is played by two persons. Two piles of counters are placed on a table, the number of each pile being arbitrary. The players play alternately and either take from one of the piles an arbitrary number of counters or from both piles an equal number. The player who takes up the last counter or counters, wins.” This game was previously known …

De Bruijn Cycles, Val Adams

Department of Mathematics: Master of Arts in Teaching, Exam Expository Papers

Problem 1. A robot is moving on a cyclic track. The track is marked at evenly spaced intervals with 0s and 1s, with a total of 8 marks. The robot can see the 3 marks closest to him. How should the 0s and 1s be put on the track so that the robot knows where on the track he is by just looking at the 3 closest marks?

Problem 2. The city of Konigsberg, Prussia is set on the Pregel River and includes two large islands, which are connected to each other and the mainland by seven bridges. Is it …

The Game Of Bridg-It, Sandy Dean

Department of Mathematics: Master of Arts in Teaching, Exam Expository Papers

On the surface, Bridg-It appears to be a simple game of connecting dots to form lines across the board. Playing Bridg-It is simple. Understanding and playing Bridg-It well is more complicated. To understand the theory and strategy behind Bridg-It, one must first understand certain elements of graph theory, such as disjoint spanning trees. Only then can one master the game of Bridg-It.

The Kaprekar Routine, Emy Jones

Department of Mathematics: Master of Arts in Teaching, Exam Expository Papers

There is a story about a man named “Joe” whose wife sent him to the supermarket. Joe was never a very good listener – he tended to pick up on the major points of a conversation, but never seemed to get things in the right order. So when he arrived at the store, he headed straight for the garlic section (for he was sure that his wife had mentioned garlic). However, when he got there, he stared at the $10 bill in his hand. She had asked him to buy $4.95 worth of garlic, or was it $9.54, or maybe …

An Uphill Battle: Incorporating Cooperative Learning Using A Largely Individualized Curriculum, Anna Anderson

Action Research Projects

In this action research study of my classroom of 8th grade mathematics, I investigated if cooperative learning could be an effective teaching method with the Saxon curriculum. Saxon curriculum is largely individualized in that most lessons could be completed without much group interaction. I discovered that cooperative learning was very successful with the curriculum as long as it was structured. Ninety-five percent of the students in the study preferred to work in groups, and I observed mathematical communication grow with most of the students. As a result of this research, I plan to continue to incorporate cooperative learning into my …

Vocabulary Instruction As A Tool For Helping Students Of Diverse Backgrounds And Ability Levels To Understand Mathematical Concepts, Joan Brethouwer

Department of Teaching, Learning, and Teacher Education: Master of Arts in Teaching, Summative Projects

This action research project describes a research project designed and implemented specifically with an emphasis on the instruction of mathematical vocabulary. The targeted population was my second period classroom of sixth grade students. This group of seventeen students represented diverse socioeconomic backgrounds and abilities. The school is located in a community of a population of approximately 5,000 people in the Midwest. My research investigation focused on the use of specific methods of vocabulary instruction and students’ use of precise mathematical vocabulary in writing and speaking. I wanted to see what effects these strategies would have on student performance. My research …

Writing Relevant Word Problems: Seeking To Increase Student Mathematical Achievement, Amanda Stark

Department of Teaching, Learning, and Teacher Education: Master of Arts in Teaching, Summative Projects

In this action research study of eighth grade mathematics, I investigated my students’ use of writing and solving word problems. I collected data to determine if writing and solving word problems would have a positive effect on students’ abilities to understand and solve word problems. These word problems are grade-level appropriate and are very similar to the problems on the eighth grade online assessment of state standards. Pre- and post-test data, weekly word problems that focus on specific mathematics topics, beginning and end surveys about word problem perceptions, and a teacher journal reveal that student engagement in this weekly practice …

Five Processes Of Mathematical Thinking, Toni Scusa

Department of Teaching, Learning, and Teacher Education: Master of Arts in Teaching, Summative Projects

My research project was to investigate key processes of mathematical thinking in my seventh grade mathematics classroom. Its purpose was to see whether I could affect the quality of student mathematical thinking and solution writing by teaching students five key processes of mathematical thinking I had identified, and by providing students with opportunities to evaluate sample student solutions using traits describing these processes. Every two weeks, students attempted solutions for a given problem and rated their work according to the specific characteristics identified as key to mathematical thinking. Every other week I gave the class sample student work at varied …

Using Non-Traditional Activities To Enhance Mathematical Connections, Sandy Dean

Action Research Projects

In this action research study of my classroom of seventh grade mathematics, I investigated the use of non-traditional activities to enhance mathematical connections. The types of nontraditional activities used were hands-on activities, written explanations, and oral communication that required students to apply a new mathematical concept to either prior knowledge or a realworld application. I discovered that the use of non-traditional activities helped me reach a variety of learners in my classroom. These activities also increased my students’ abilities to apply their mathematical knowledge to different applications. Having students explain their reasoning during non-traditional activities improved their communications skills, both …

Using Descriptive Feedback In A Sixth Grade Mathematics Classroom, Vicki J. Barry

Action Research Projects

In this action research of my 6th grade math class, I investigated whether or not my students would improve their ability to reflect on their learning process when they received descriptive feedback from a peer. I discovered the process of giving and receiving feedback was challenging for the students to initially learn, but eventually using the feedback was highly beneficial. Descriptive feedback allowed the students to learn and understand their mistakes immediately, which in turn improved their learning. In my action research, I also began to discover more ways to implement descriptive feedback in my instruction so it could be …

Calculators In A Middle School Mathematics Classroom: Helpful Or Harmful?, Leah Wilcox

Action Research Projects

In this action research study of my classroom of eighth grade mathematics, I investigated the use of calculators. Specifically, I wanted to know the answer to three questions. I wanted to know more about what would happen to my students’ ability to recall basic math facts, their ability to communicate mathematically during problem solving, and their attitude when my students were or were not permitted to use their calculator. I discovered that in my research, I did not find enough evidence to either support or reject my initial hypotheses, that calculators largely influenced my students’ behavior, and also that my …

Rubric Assessment Of Mathematical Processes In Homework, Aubrey Weitzenkamp

Action Research Projects

In this action research study of my classroom of 11th grade geometry, I investigated the use of rubrics to help me assess my students during homework presentations. I wanted to know more about the processes students went through as they did their homework problems, so homework presentations were implemented with the rubrics being the main form of assessment. I discovered that students are willing to speak about mathematics and can gain more understanding of mathematical processes as a result of homework presentations. The scores of the class improved after they talked about the homework assignments with each other. As a …

Rap (Reasoning And Proof) Journals: I Am Here, Bryce Schwanke

Action Research Projects

In this action research study of my classroom of 5th grade mathematics, I investigated writing in a journal as formative assessment. I also investigated how elementary age students would be able to utilize the National Council of Teachers of Mathematics (NCTM) process standard reasoning and proof. Using the Houghton Mifflin (2005) textbook and curriculum I discovered that writing reasons and proof as a formative assessment in a mathematics journal is a good way to teach mathematics. Having students solve math problems during the closure portion of each math lesson does a good job of holding students accountable for the math …

How Student Self-Assessment Influences Mastery Of Objectives, Jeremy John Renfro

Action Research Projects

In this action research study of my classroom of 7th grade students, enrolled in Pre- Algebra (an 8th grade course), I investigated: rate of homework completion when not taken as part of the academic grade, cognizant self-assessment and its affect on mastery of objectives, and use of self-assessment to guide instruction and re-teaching of classroom objectives. I learned that without sufficient accountability homework completion rates drop with time. Similarly, students can be overconfident in their abilities but unmoved when their summative reports do not match their initial perceived formative benchmarks. Finally, due in part to our society’s reactive nature; students …

Ua64/2 The Challenge: Magazine Of The Center For Gifted Studies (No. 21, Summer 2008), Center For Gifted Studies, Tracy Inman Editor

Gifted Studies Publications

No abstract provided.

Enough Already? Linking Science, Geography, Mathematics, And Sociology Through Population Study, Roxanne Greitz Miller, Lilian M. Were

Education Faculty Articles and Research

In several previous Issues In-Depth columns, science topics deeply affected by population size--such as climate change, fuel and agricultural resources, and ecology--have been discussed. In this column, we will discuss the issue of population growth in developed and developing countries, why this is an important topic to discuss with young adolescents, and how interdisciplinary connections can be made between science and several other subject areas through an examination of populations across the globe.

Producing More Problem Solving By Emphasizing Vocabulary, Jill Edgren

Action Research Projects

In this action research study of my Algebra 1 and Algebra 2 classrooms with ninth to eleventh grade students, I investigated word problem completion while emphasizing vocabulary. A word wall was implemented along with notes organizers, vocabulary sheets, and written definition during class. Data was gathered about attempts and completion of mathematic word problems on daily assignments, quizzes, journals and tests. Through observation of student work, surveys, interviews, and in class word problem journals, I discovered that many students are least likely to do word problems on assignments, then tests, and most likely to complete word problems on a quiz. …

Mathematical Communication, Conceptual Understanding, And Students' Attitudes Toward Mathematics, Kimberly Hirschfeld-Cotton

Action Research Projects

This action research study of my 8th grade classroom investigated the use of mathematical communication, through oral homework presentations and written journals entries, and its impact on conceptual understanding of mathematics. This change in expectation and its impact on students’ attitudes towards mathematics was also investigated. Challenging my students to communicate mathematics both orally and in writing deepened the students’ understanding of the mathematics. Levels of understanding deepened when a variety of instructional methods were presented and discussed where students could comprehend the ideas that best suited their learning styles. Increased understanding occurred through probing questions causing students to reflect …

Building Confidence In Low Achievers Through Building Mathematics Vocabulary, Val Adams

Action Research Projects

In this action research study, I investigated the use of vocabulary strategies and the effectiveness of the strategies in building confidence in low achievers. My subjects were twenty-three eighth grade mathematics students. They were introduced to vocabulary activities and then were asked to use them in class through the use of note-taking graphic organizers, group class discussion, and partner work. I assessed their confidence and use of vocabulary through a pre and post survey, class work, notebook checks, and student interviews. I discovered that the use of vocabulary strategies built the confidence and increased the achievement of my students. As …

Does Decoding Increase Word Problem Solving Skills?, Jalena J. Clement

Action Research Projects

In this action research study of my classroom of 7th grade mathematics, I investigated whether the use of decoding would increase the students’ ability to problem solve. I discovered that knowing how to decode a word problem is only one facet of being a successful problem solver. I also discovered that confidence, effective instruction, and practice have an impact on improving problem solving skills. Because of this research, I plan to alter my problem solving guide that will enable it to be used by any classroom teacher. I also plan to keep adding to my math problem solving clue words …