Science and Mathematics Education Commons^™

Motivation And Performance In Computer Science: Test Of An Integrative Theory, Katherine A. Selgrade

Psychology Theses & Dissertations

The purpose of this study was to design and empirically test a parsimonious integrative motivation theory. The theory integrates aspects of expectancy theory, social cognitive theory, goal-setting theory, and commitment theory. The theory was tested with 170 undergraduate, students in an introductory computer science (CS) course.

The study tested relationships among the following variables: CS self-efficacy, mathematics ability, affective commitment to the CS class, goal orientation, effort, and performance. The study also tested the interactive effects of effort and ability on performance. Structural equation modeling was used to test the measurement model and a series of nested structural models. Findings …

The Importance Of Teaching Students How To Read To Comprehend Mathematical Language, Tricia Buchanan

Action Research Projects

In this action research study of my classroom of 8th and 9th grade Algebra I students, I investigated if there are any benefits for the students in my class to learn how to read, translate, use, and understand the mathematical language found daily in their math lessons. I discovered that daily use and practice of the mathematical language in both written and verbal form, by not only me but by my students as well, improved their understanding of the textbook instructions, increased their vocabulary and also increased their understanding of their math lessons. I also found that my students remembered …

Pre-Reading Mathematics Empowers Students, Stacey Aldag

Action Research Projects

In this action research study of my 8th grade mathematics classroom, I investigated the improvement of mathematical communication via assigning pre-reading material and requiring students to take notes prior to class discussions. I discovered that students became more active participants during classroom discussions and were able to produce work which illustrated their mathematical understanding. Teacher observations and improved quiz scores provide quantitative evidence, and student survey responses validate student communication. As a result of this research, I plan to assign pre-reading tasks and require students to take notes prior to class discussions with the goal to change classroom presentation from …

Improving The Effectiveness Of Independent Practice With Corrective Feedback, Greg Vanderbeek

Action Research Projects

In this action research study of my 8th grade Algebra class, I investigated the effects of teacher-to-student written corrective feedback on student performance and attitude toward mathematics. The corrective feedback was given on solutions for selected independent practice problems assigned as homework. Each problem being assessed was given a score based on a 3- point rubric and additional comments were written. I discovered that providing teacher-to-student written corrective feedback for independent practice problems was beneficial for both students and teachers. The feedback positively affected the attitudes of students and teacher toward independent practice work resulting in an improved quality of …

Increasing Teacher Involvement With Other Teachers Through Reflective Interaction, Tina Thompson

Action Research Projects

In this action research study of a district’s mathematics teachers, the researcher investigated how teachers interact with other teachers in their building and throughout the district. The researcher wanted to know how deeply teachers thought about teaching mathematics, and if they use other teachers in the district as a resource to help with unknown math problems. The researcher discovered that some teachers are willing to interact with others, but would like to have time supplied to them during the school year’s staff development meetings. The teachers involved were able to observe each other teaching and take valuable strategies back to …

Why Are We Writing? This Is Math Class!, Shana Streeks

Action Research Projects

In this action research study of my classroom of 8th grade mathematics, I investigated writing in the content area. I have realized how important it is for students to be able to communicate mathematical thoughts to help gain a deeper understanding of the content. As a result of this research, I plan to enforce the use of writing thoughts and ideas regarding math problems. Writers develop skills and generate new thoughts and ideas every time they sit down to write. Writing evolves and grows with ongoing practice, and that means thinking skills mature along with it. Writing is a classroom …

Effects Of Self-Assessment On Math Homework, Diane Swartzlander

Action Research Projects

In this action research study of my eighth grade differentiated Algebra students, I investigated the effects of students using self-assessment on their homework. Students in my class were unmotivated and failed test objectives consistently. I wanted students to see that they controlled their learning and could be motivated to succeed. Formative assessment tells students how they need to improve. Learning needs to happen before they can be assessed. Self-assessment is one tool that helps students know if they are learning. A rubric scoring guide, daily documentation sheet and feedback on homework and test correlations were used to help students monitor …

Do Students Progress If They Self-Assess? A Study In Small-Group Work, Cindy Steinkruger

Action Research Projects

In this action research study of my classroom of 8th grade mathematics, I investigated the effects of self-assessment on student group work. Data was collected to see how self-assessment affected small-group work, usage of precise mathematical vocabulary, and student attitudes toward mathematics. Self-assessment allowed the students to periodically evaluate their own learning and their involvement in math class. I discovered that the vast majority of students enjoy working in small-groups, and they feel they are good group members. Evidence in regard to use of precise mathematical vocabulary showed an increased awareness in the importance of its usage. Student attitudes toward …

Improving Student Engagement And Verbal Behavior Through Cooperative Learning, Daniel Schaben

Action Research Projects

In this action research study of my classroom of 10th grade Algebra II students, I investigated three related areas. First, I looked at how heterogeneous cooperative groups, where students in the group are responsible to present material, increase the number of students on task and the time on task when compared to individual practice. I noticed that their time on task might have been about the same, but they were communicating with each other mathematically. The second area I examined was the effect heterogeneous cooperative groups had on the teacher’s and the students’ verbal and nonverbal problem solving skills and …

Improving Student Engagement And Verbal Behavior Through Cooperative Learning, Daniel Schaben

Action Research Projects

In this action research study of my classroom of 10th grade Algebra II students, I investigated three related areas. First, I looked at how heterogeneous cooperative groups, where students in the group are responsible to present material, increase the number of students on task and the time on task when compared to individual practice. I noticed that their time on task might have been about the same, but they were communicating with each other mathematically. The second area I examined was the effect heterogeneous cooperative groups had on the teacher’s and the students’ verbal and nonverbal problem solving skills and …

Writing For Understanding In Math Class, Linda Moore

Action Research Projects

In this action research study of my classroom of 10th grade geometry students, I investigated how students learn to communicate mathematics in a written form. The purpose of the study is to encourage students to express their mathematical thinking clearly by developing their communication skills.

I discovered that although students struggled with the writing assignments, they were more comfortable with making comments, writing questions and offering suggestions through their journal rather than vocally in class. I have utilized teaching strategies for English Language Learners, but I had never asked the students if these strategies actually improved their learning. I have …

Testing Naval Artillery And Other Things, Tricia Buchanan

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

In WWII a tremendous amount of artillery shells were made to support the war efforts. There were problems with the artillery shells sent to the battlefield; the main problem was their lack of ability to blow things up. In other words, they were duds! While one may think that dud shells were the proverbial rare case, in my paper I hope to show you that instead it unfortunately seemed more the norm. The reasons behind this are varied but in this paper I will focus on the testing practices of the artillery shells and some of the issues that occurred …

Jean Baptiste Joseph Fourier, Gary Eisenhauer

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

Jean Baptiste Joseph Fourier was born in Auxerre, France on March 21, 1768. He was the ninth of twelve children from his father’s second marriage. When he was nine, his mother died. The following year, his father, a tailor, also passed.

Extending A Finite Sequence, Jessica Fricke

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

One of the most common mistakes in school mathematics is to list a few terms of a sequence and ask “What term comes next?” For example, a teacher may write: 1 2 4 … and ask what term comes next? The best answer is “almost anything could be the next term.” But people often find that answer unsatisfying. It helps, instead, to give an example. Perhaps, one might respond by saying: “The next number might be 8, but then again, it might be 7.” This answer might, of course, result in an angry teacher, so you need to be prepared …

Ethnomathematics, Chad Larson

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

When asked to think about a foreign country the first thing that comes to my mind is the language barrier and the customs that accompany that specific country. The culture of the citizens and how it differs from my culture are also things which peak my interest. Things which I view as “normal” may seem very odd to someone who lives thousands of miles away, and likewise, traditions that have been past down from generations of people from distant lands may seem peculiar to me. These customs and cultures of which I speak are also the things that make this …

Experimentation With Two Formulas By Ramanujan, Daniel Schaben

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

Srinivasa Ramanujan was a brilliant mathematician, considered by George Hardy to be in the same class as Euler, Gauss, and Jacobi. His short life, marred by illness and tragic educational events, was unique in the history of mathematics. Mathematical discoveries are still being gleaned from his personal notebooks. Paper was a hard commodity to come by so his notebooks were a cluttered mix of pen over pencil mathematical hieroglyphics. The following highlights Ramanujan’s life in connection with Hardy, his work with ellipses, and his work with the partition function.

Simple Statements, Large Numbers, Shana Streeks

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

Large numbers are numbers that are significantly larger than those ordinarily used in everyday life, as defined by Wikipedia (2007). Large numbers typically refer to large positive integers, or more generally, large positive real numbers, but may also be used in other contexts. Very large numbers often occur in fields such as mathematics, cosmology, and cryptography. Sometimes people refer to numbers as being “astronomically large”. However, it is easy to mathematically define numbers that are much larger than those even in astronomy. We are familiar with the large magnitudes, such as million or billion. In mathematics, we may know a …

The Four Numbers Game, Tina Thompson

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

The Four Numbers Game is a fun way to work with subtraction and ordering of numbers. While trying to find an end to a game that is played with whole numbers, there are several items that will be investigated along the way. First, we offer an introduction to how the game is played. Second, rotations and reflections of a square will be presented which will create a generalized form. Third, we explain how even and odd number combinations will always end in even numbers within four subtraction rounds. Fourth, we argue that the length of the game does not change …

Distance, Rate, Time And Beyond, Janet Timoney

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

In middle school mathematics, students learn to use the formula “distance equals rate times time,” usually expressed as d = r × t. Why not consider the formula distance = velocity × time? Does the term velocity mean something different than the term rate? We could also consider the variations of these formulas: distance ÷ time = rate, or distance ÷ rate = time. We can examine the definitions of these words and words which are very similar. After looking at the definitions of these words, maybe we will have a better understanding of how to use the formulas and …

Order Of Operations And Rpn, Greg Vanderbeek

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

There is not a wealth of information regarding the history of the notations and procedures associated with what is now called the “order of operations”. There is evidence that some agreed upon order existed from the beginning of mathematical study. The grammar used in the earliest mathematical writings, before mathematical notation existed, supports the notion of computational order (Peterson, 2000). It is clear that one person did not invent the rules but rather current practices have grown gradually over several centuries and are still evolving.

The Use Of Think-Aloud Strategies To Solve Word Problems, Lisa M. Henjes

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

In this action research study of my sixth grade mathematics class, I investigated how students’ use of think-aloud strategies impacts their success in solving word problems. My research reveals that the use of think-aloud strategies can play an important role in the students’ abilities to understand and solve word problems. Direct instruction and modeling of think-aloud strategies increased my students’ confidence levels and the likelihood that they would use the strategies on their own. Providing students with a template to use as they solve a word problem helps students to better focus in on the think-aloud strategies I had been …

Writing In The Mathematics Classroom: Does It Have An Effect On Students’ Mathematical Reasoning?, Rachel Bunnett

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

In this action research study of my classroom of 5th grade mathematics, I investigate how to improve students’ written explanations to and reasoning of math problems. For this, I look at journal writing, dialogue, and collaborative grouping and its effects on students’ conceptual understanding of the mathematics. In particular, I look at its effects on students’ written explanations to various math problems throughout the semester. Throughout the study students worked on math problems in cooperative groups and then shared their solutions with classmates. Along with this I focus on the dialogue that occurred during these interactions and whether and how …

It Is Not Just The Solution Anymore, Carol Brown

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

In this action research study of a fifth grade enrichment mathematics class, I investigate how problem solving strategies and group work opportunities influence the students’ use of strategies and graphic representations. Though there are no large gains in the students’ use of strategies, some students show minor gains in their use of representations. I also investigate the influence of group work upon usage of representations. At the beginning of the study most students indicate that working in groups is helpful in finding solutions. Toward the end, 52.9 percent of the students indicate that while group work is beneficial for “reasoning” …

A Study Of Written Communication: Showing Your Steps, Megan Kelly

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

In this action research study of my teaching of sixth grade mathematics, I investigated the importance of showing work on daily assignments. I wanted to find out what happens when I ask students to show their work, specifically, whether it would improve students’ grades or not and whether I could help the students to understand the importance of showing their work. I discovered that students need to be shown the proper way to show their work, how to look at a problem and then how to show all of their steps to get to the answer. They need to be …

Building Math Esteem In Fifth Grade Students, Karen Schur

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

In this action research study of my classroom of 5th grade mathematics, I investigate the levels of math esteem in each student and as a classroom. The definition of esteem on which I am basing my research is the judgment or estimation of the self-assurance of a student in math. I discovered that several of the students entered my classroom with a middle to low level of esteem in math, and about a third of the class already exhibited a positive, high esteem in math. After implementation of the research, and interpreting the data, I believe almost all the students …

Increasing Student Confidence And Knowledge Through Student Presentations, Lori Ziemba

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

In this action research study of a 9th grade Algebra classroom, I investigated the influence of having students present homework solutions and what effect it had on student learning and student confidence. Students were asked to present solutions to homework problems each day and were rated on how well they did. The students were also surveyed about their confidence and feelings about mathematics. Students were also observed for information about who they asked questions of when presented with a math problem they did not understand. In this classroom, two teachers were involved in instruction and this study examines what affect …

An Investigation Into Careless Errors Made By 7th Grade Mathematics Students, Andrea Wiens

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

In this action research study, I investigated the careless errors made by my seventh-grade mathematics students on their homework and tests. Beyond analyzing the types of careless errors and the frequency at which they were made, I also analyzed my students’ attitudes toward reviewing their work before they turn it in and self-reflection about the quality of work that they were producing. I found that many students did not know how to review their test before turning it in; no one had ever taught them how to do so. However, when students were given tools to help them with this …

Here Is The Plan: So What Is The Question?, Dot Snesrud

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

In this action research study of my classroom of 5th grade mathematics students, I investigated their understanding of the mathematical operations by having them write problems to match given equations. I discovered that writing a story to match an equation does provide insight into a student’s understanding of mathematical concepts, however, reading comprehension is a factor in the understanding. Readers who struggle with comprehension do struggle with understanding and writing math story problems. The discussion that follows the writing of a math story problem and the solving of the written problems helps to strengthen the students’ mathematical abilities as well …

Algebraic Geometric Codes On Anticanonical Surfaces, Jennifer A. Davis

Department of Mathematics: Dissertations, Theses, and Student Research

Algebraic geometric codes (or AG codes) provide a way to correct errors that occur during the transmission of digital information. AG codes on curves have been studied extensively, but much less work has been done for AG codes on higher dimensional varieties. In particular, we seek good bounds for the minimum distance.

We study AG codes on anticanonical surfaces coming from blow-ups of P² at points on a line and points on a conic. We can compute the dimension of such codes exactly due to known results. For certain families of these codes, we prove an exact result on …

Teach A Course In The Math Of Voting And Choice, Karl-Dieter Crisman

ACMS Conference Proceedings 2007

Many mathematics instructors at the college level are looking for a curricular option that has the potential to serve a number of different constituencies. It could be to encourage more students to take math courses, or to give worthwhile options to students who need to take math but who are not ready for calculus (or its sequence). On the other hand, one may wish to add a new course for majors outside of the typical offerings, or even to prepare students for undergraduate research. The mathematics of voting and choice is ideally suited to meet all these needs in the …