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Math In The Middle Newsletter December 2008

Math in the Middle Program Materials

NebraskaMATH is Now Seeking Applications
Primarily Math
Nebraska Algebra: Extending Success to All Students
Retaining Quality Teachers (RQT)
New Additions

Math In The Middle Newsletter November 2008

Math in the Middle Program Materials

NebraskaMATH Update
M2 Newsletter to Evolve January 2009
NTV Teacher of the Month: Cohort 4’s Michael Ford
A Must-Read for Habits of Mind Problem Seekers
Math Challenge Corner: What do soccer balls and equilateral triangles have in common?

Math In The Middle Newsletter October 2008

Math in the Middle Program Materials

NEBRASKA MATH by Jim Lewis

Host a NU-Teach Course at your ESU!

Omaha Public Schools to Partner with Math in the Middle

A Theory Of Non-Noetherian Gorenstein Rings, Livia M. Miller

Department of Mathematics: Dissertations, Theses, and Student Research

In Noetherian rings there is a hierarchy among regular, Gorenstein and Cohen-Macaulay rings. Regular non-Noetherian rings were originally defined by Bertin in 1971. In 2007, Hamilton and Marley used Cech cohomology to introduce a theory of Cohen-Macaulay for non-Noetherian rings, answering a question posed by Glaz. This dissertation provides a theory of non-Noetherian Gorenstein rings agreeing with the Noetherian definition, and for which regular rings are Gorenstein, and coherent Gorenstein rings are Cohen-Macaulay. The relationship between Gorenstein rings and FP-injective dimension as defined by Stenstrom is also explored. Finally, an additional characterization of Gorenstein rings involving homological dimensions is examined …

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 …

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 …

Exploring The Influence Of Vocabulary Instruction On Students’ Understanding Of Mathematical Concepts, Micki Mcconnell

Action Research Projects

In this action research study of my classroom of 8th grade mathematics, I investigated the influence of vocabulary instruction on students’ understanding of the mathematics concepts. I discovered that knowing the meaning of the vocabulary did play a major role in the students’ understanding of the daily lessons and the ability to take tests. Understanding the vocabulary and the concepts allowed the students to be successful on their daily assignments, chapter tests, and standardized achievement tests. I also discovered that using different vocabulary teaching strategies enhanced equity in my classroom among diverse learners. The knowledge of the math vocabulary increased …

Can Homework Become More Meaningful With The Inclusion Of Oral Presentations?, Emy Jones

Action Research Projects

In this action research study of my 7th grade math class, I investigated the inclusion of homework presentations to see if they would improve students’ attitude toward mathematics, participation, and understanding. I discovered that although the implementations of presentations into our homework routine did not drastically influence grades, or even improve attitudes (according to test grades and student surveys), a multitude of other changes surfaced. These changes consisted of an increase in discussion, a team effort among students in my class, and an overall “learning community” effect. I plan to continue to pursue presentations as a major part of my …

Enhancing Thinking Skills: Will Daily Problem Solving Activities Help?, Julie Hoaglund

Action Research Projects

In this action research study of my classroom of eighth grade general mathematics students, I investigated how addressing problem solving activities each day would affect the thinking and reasoning skills of the students. I discovered that the students became more adept at problem solving as they practiced various strategies. As students justified their answers, both orally and in written form, their understanding of mathematics and its applications to the real world improved. I discovered that students worked more diligently on problems of interest to them. Also, some problems are better solved individually, and some are more geared as a group …

Summarization In Math Class, Scott Eckman

Departament of Teaching, Learning, and Teacher Education: Master's of Arts in Teaching, Summative Projects

This action research study of twenty students in my sixth grade mathematics classroom examines the implementation of summarization strategies. Students were taught how to summarize concepts and how to explain their thinking in different ways to the teacher and their peers. Through analysis of students’ summaries of concepts from lessons that I taught, tests scores, and student journals and interviews, I discovered that summarizing mathematical concepts offers students an engaging opportunity to better understand those concepts and render that understanding more visible to the teacher. This analysis suggests that non-traditional summarization, such as verbal and written strategies, and strategies involving …

Five Processes Of Mathematical Thinking, Toni Scusa

Departament of Teaching, Learning, and Teacher Education: Master's 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 …

A Study Of The Summarization Of Word Problems, Tara Schwanebeck

Departament of Teaching, Learning, and Teacher Education: Master's of Arts in Teaching, Summative Projects

This action research investigates my sixth grade mathematics students’ ability to solve word problems after instruction and practice using a specific word problem summarization worksheet. The worksheet was designed to break down word problems into smaller parts, helping students comprehend them and, in turn, find success that would enhance their confidence and ability to successfully solve word problems. The worksheets each had a different type of word problem, such as one-step, hidden information, or extra information. The final worksheet consisted of a mixed review of each type of word problem previously practiced in class. Using different types of data collection …

Wythoff’S Game, Kimberly Hirschfeld-Cotton

Department of Mathematics: Master's 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 …

The Game Of Bridg-It, Sandy Dean

Department of Mathematics: Master's 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 Polar Coordinate System, Alisa Favinger

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

Representing a position in a two-dimensional plane can be done several ways. It is taught early in Algebra how to represent a point in the Cartesian (or rectangular) plane. In this plane a point is represented by the coordinates (x, y), where x tells the horizontal distance from the origin and y the vertical distance. The polar coordinate system is an alternative to this rectangular system. In this system, instead of a point being represented by (x, y) coordinates, a point is represented by (r, θ) where r represents the length of a straight line from the point to the …

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 …

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 …

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. …

Reduce Late Assignments Through Classroom Presentations, Cole Hilker

Action Research Projects

In this action research study of my 7th grade math class, I investigated homework presentations, to see if they would reduce the amount of late homework assignments. I did not find any significant results that weekly presentations given by students were beneficial to reduce the amount of late assignments, but found many other positive things that happened because of presentations. As a result of this research, I plan to use classroom presentations because they foster listening skills and student interaction, and promote deeper thinking.

Using Relearning Groups To Help All Students Understand Learning Objectives Before Tests, Katie Pease

Action Research Projects

In this action research study of my 8th grade algebra class, I investigated placing students in relearning groups based on learning objectives. A learning objective is what a learner should be able to do by the end of a learning experience. I was trying to see how this affected test scores, anxiety in the classroom and on tests, and how it affected my teaching. Overall, I discovered that the relearning groups were beneficial. Many students stated the extra practice helped them perform better and feel slightly less nervous than they originally had before a test. I did not discover the …

Cooperative Learning In Relation To Problem Solving In The Mathematics Classroom, Shelley Poore

Action Research Projects

In this action research study of my classroom of 5th grade mathematics, I investigated cooperative learning and how it is related to problem solving as well as written and oral communication. I discovered that cooperative learning has a positive impact on students’ abilities in problem solving and their overall impression of mathematics and group work. I also found that my students’ communication skills improved in oral explanations of their work. As a result of this research I plan to continue my implementation of cooperative learning in my classroom as a general method of teaching. I also plan to continue to …

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 …

Homework: Is There More To It Than Answers?, Shelly Sehnert

Action Research Projects

In this action research study of my two high school geometry classrooms, I investigated the use of homework. By changing the focus on homework away from the answers to the process involved in getting the answers, I found that students felt more confident, utilized their class time better, and placed more effort on complex problems. Their questions also became more specific and more effective for finding gaps in their understanding. As a result of this research, I plan to change my strategy in the practice of homework. I will give students the answers on multi-step problems to allow them the …

De Bruijn Cycles, Val Adams

Department of Mathematics: Master's 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 …

Archimedean Solids, Anna Anderson

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

A polygon is a simple, closed, planar figure with sides formed by joining line segments, where each line segment intersects exactly two others. If all of the sides have the same length and all of the angles are congruent, the polygon is called regular. The sum of the angles of a regular polygon with n sides, where n is 3 or more, is 180° x (n – 2) degrees. If a regular polygon were connected with other regular polygons in three dimensional space, a polyhedron could be created. In geometry, a polyhedron is a threedimensional solid which consists of a …

Mathematics And Evolution, Kacy Heiser

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

What is game theory and how does it apply to Evolutionary Biology? Game theory was originally developed to help portray how individuals interact with each other and it was mainly used in the economics and political science fields. This area of mathematical study came about after World War II and was developed by John von Neumann and Oskar Morgenstern. It wasn’t until the 1970’s that George Price and John Maynard Smith began to apply game theory to evolution in trying to predict the behavior of animals in a species. There are two main evolutionary trends we will study using game …

Lester’S Circle, Julie Hoaglund

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

Euclid is credited with most of the theorems in geometry textbooks today. Around 300 B.C., Euclid produced a thirteen volume publication called The Elements. These volumes include much information others had studied. Throughout history, many great mathematicians including Pasch, Hilbert, and Birkhoff have studied and tried to improve Euclidean geometry. Groups such as University of Chicago School Mathematics Project have made improvements on the Euclid’s axiomatic system.

The Kaprekar Routine, Emy Jones

Department of Mathematics: Master's 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 …

Precise Mathematical Language: Exploring The Relationship Between Student Vocabulary Understanding And Student Achievement, Jill Kranda

Departament of Teaching, Learning, and Teacher Education: Master's of Arts in Teaching, Summative Projects

In this action research study of my classroom of fifth grade mathematics, I investigate the relationship between student understanding of precise mathematics vocabulary and student achievement in mathematics. Specifically, I focused on students’ understanding of written mathematics problems and on their ability to use precise mathematical language in their written solutions of critical thinking problems. I discovered that students are resistant to change; they prefer to do what comes naturally to them. Since they have not been previously taught to use precise mathematical language in their communication about math, they have great difficulty in adapting to this new requirement. However, …

Improving Communication About Mathematics Through Vocabulary And Writing, Kelly Georgius

Departament of Teaching, Learning, and Teacher Education: Master's of Arts in Teaching, Summative Projects

In this action research study, where the subjects were my 6th grade mathematics students, I investigated the impact of direct vocabulary instruction on their communication and achievement. I strategically implemented the addition of vocabulary study into each lesson over a four-month time period. The students practiced using vocabulary in verbal discussions, review activities, and in mathematical problem explanations. I discovered that a majority of students improved their overall understanding of mathematical concepts based on an analysis of the data I collected. I also found that in general, students felt that knowing the definition of mathematical words was important and that …