Education Commons^™

Math In The Middle Report To Nebraska December 2009

Math in the Middle Program Materials

Table of Contents:

An overview of Math in the Middle

Gordon-Rushville reaps benefits of Math in the Middle

Nebraska Math & Science Summer Institutes: Courses enhance teaching abilities

Math in the Middle graduates excel as teacher leaders

Math in the Middle graduate achievements: Exemplary leaders in math education

Dan Schaben, former NATM president, reflects on Math in the Middle

Math Teachers’ Circle: The drive to learn continues

Action Research Papers

Math Expository Papers

Doctoral Students and Math in the Middle

Selected Publications

Contributors: Jim Lewis, Ruth Heaton, Michelle Homp, Wendy Smith, Shannon Parry and Lindsay Augustyn

Design/Layout: Lindsay Augustyn

Nebraskamath December 2009 Newsletter

NebraskaMATH Materials

NebraskaMATH December 2009 Newsletter

Table of Contents:

Nebraska Summit on Mathematics Education speakers inspire audience

Nebraskamath November 2009 Newsletter

NebraskaMATH Materials

NebraskaMATH November 2009 Newsletter

Table of Contents:

Common Core State Standards

NE Summit on Mathematics Education

NE Algebra accepts applications

NCTM seeks articles from teachers

New Central NE Math Teachers’ Circle

Highlight on Action Research

Resource: Teaching Teachers Mathematics

UNL Math Day on Nov. 12

Encomium: Rolliin Harold Baker: 1916-2007, Carleton J. Phillips, Robert J. Baker, Hugh H. Genoways

University of Nebraska State Museum: Mammalogy Papers

Rollin H. Baker passed away on November 12, 2007, one day after reaching his 91st birthday. Rollin was a living legend, famous for his pioneering research on biogeography and natural history of Mexican mammals, especially rodents, for his contributions to the understanding of Michigan mammals, and for being a mentor and friend to all young, aspiring mammalogists. Rollin Baker’s career lasted way beyond his traditional retirement, and in his final months he was still active in the Texas Society of Mammalogists and in conservation issues in Texas. Indeed, when he was 89 years old he presented a guest lecture in …

Nebraskamath October 2009 Newsletter

NebraskaMATH Materials

NebraskaMATH October 2009 Newsletter

Table of Contents

Progress Report on the Revised Nebraska Mathematics Standards

Joint Meeting of Nebraska’s Ed Leaders

NE Summit on Mathematics Education

Math Challenge Corner

Resources

Common Core Standards

Nebraskamath September 2009 Newsletter

NebraskaMATH Materials

NebraskaMATH September 2009 Newsletter

Table of Contents:

Fast Moving Educational Initiatives

NebraskaMATH Summer Activities

Book Review

Math Quote

Highlight on Action Research

Math in the Middle Cohort 4 Graduation

A Computational Study Of The Effects Of Temperature Variation On Turtle Egg Development, Sex Determination, And Population Dynamics, Amy L. Parrott

Department of Mathematics: Dissertations, Theses, and Student Research

Climate change and its effects on ecosystems is a major concern. For certain animal species, especially those that exhibit what is known as temperature-dependent sex determination (TSD), temperature variations pose a possibly serious threat (Valenzuela and Lance, 2004). In these species, temperature, and not chromosomes, determines the sex of the animal (Valenzuela and Lance, 2004). It is conceivable therefore, that if the temperature changes to favor only one sex, then dire consequences for their populations could occur. In this dissertation, we examine possible effects that climate change may have upon Painted Turtles (Chrysemys picta), a species with TSD. We investigate …

Fan Cohomology And Equivariant Chow Rings Of Toric Varieties, Mu-Wan Huang

Department of Mathematics: Dissertations, Theses, and Student Research

Toric varieties are varieties equipped with a torus action and constructed from cones and fans. In the joint work with Suanne Au and Mark E. Walker, we prove that the equivariant K-theory of an affine toric variety constructed from a cone can be identified with a group ring determined by the cone. When a toric variety X(Δ) is smooth, we interpret equivariant K-groups as presheaves on the associated fan space Δ. Relating the sheaf cohomology groups to equivariant K-groups via a spectral sequence, we provide another proof of a theorem of Vezzosi and Vistoli: equivariant K …

Mathematical Communication Through Written And Oral Expression, Brandee Wilson

Action Research Projects

In this action research study of my classroom of sixth grade mathematics, I investigated the use of communication of mathematics through both written and oral expression. Giving my students the opportunity to communicate mathematics both in writing and orally helped to deepen the students’ understanding of mathematics. The students’ levels of comprehension were increased when they were presented with a variety of instructional methods. Through discussion and reflection the students were able to find methods that worked best for them and their learning ability. Students’ understanding increased from probing questions that made the students reflect and re-evaluate their solutions. This …

Written Communication In A Sixth-Grade Mathematics Classroom, Mary Schneider

Action Research Projects

In this action research study of my sixth grade mathematics classroom, I investigated what happened to students’ mathematical achievement when they had increased practice on written explanations to problems. I wanted to see if writing out solutions to problems helped them overall in daily mathematics. By using specific mathematic vocabulary more frequently and deliberately during my instruction, I wanted to investigate whether students would correctly use specific math vocabulary in their written explanations. I also increased my expectations of the students’ written explanations throughout the research project. I wanted to determine whether students would try to meet or even exceed …

Reviewing, Rethinking And Revising Homework Expectations In A Seventh Grade Math Class, Marilyn Hein

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

In this action research study of my seventh grade mathematics class, I investigated whether de-emphasizing homework assignments as daily grades while stressing them as daily practice encouraged students to focus more on the learning rather than the daily grade. As part of this study, I also looked at how this change in homework expectations affected my daily teaching. I discovered that having students keep notes, examples, practice problems and homework assignments in a notebook helped them concentrate more on the process of getting answers and why they may of had an incorrect answer. Students were more likely to discuss with …

Problems With Problem Solving: Assessing Written Solutions Of Mathematical Habits Of Mind Problems, Ali Arndt

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

This paper explores a study of sixth grade mathematics students in a middle school setting. I investigated the effects of assigning Habits of Mind problems related to the curriculum, district standards and objectives to increase problem-solving opportunities and skills. I discovered integrating problem solving into the given curriculum allowed students to make connections to math in an opportune way that evoked communication on paper, interactions with partners or small groups, and presentations of solutions to the large group. Using the challenging Habits of Mind problems deliberately chosen to match specific content objectives within my district at the sixth grade level …

Sudoku, Marlene Grayer

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

Many people have a magazine, a crossword puzzle, a newspaper, or a book on hand to fill idle time. I, however, prefer to tease my mind with a book of Sudoku puzzles (pronounced sue‐dah‐coup), trying to figure out what number goes where while resisting the temptation to peek in the back at the answer to make sure I am on the right track. For those of you who are unaware of what Sudoku is, it is a highly popular number game whose notoriety may even surpass the crossword or word search puzzles. It can be found in popular newspapers such …

Sicherman Dice, Scott Johnsen

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

Many different types of games involve the use of numbered dice. The most common type of die used is the standard six-sided die with the numbers one through six used on its six sides. What if there was another way of numbering a set of dice (using only positive integers) that would create the same probability outcomes as those of a standard set of dice? The February 1978 issue of Scientific American reports that George Sicherman discovered such a numbering (Broline, 1979). Sicherman discovered that two cubic die numbered 1-2-2-3-3-4 and 1-3-4-5-6-8 have the same sum probabilities as do the …

Amicable Pairs, Lexi Wichelt

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

The ancient Greeks are often credited with making many new discoveries in the area of mathematics. Euclid, Aristotle, and Pythagoras are three such famous Greek mathematicians. One of their discoveries was the idea of an amicable pair. An Amicable pair is a pair of two whole numbers, each of which is the sum of the proper whole number divisors of the other.

Forgetting To Remember: Formative Assessment In Sixth Grade Mathematics Classroom, Corie Lubash

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

In this action research study of a sixth grade mathematics classroom, I investigated what would happen to the students’ understanding of mathematical concepts and what student learning would look like when multiple formative assessments were implemented and descriptive feedback was given by the teacher. I also examined how my own teaching would be affected when I utilized descriptive feedback on formative assessments in attempts to decrease the number of retakes needed on summative assessments. I discovered that my students were better prepared for summative assessments when multiple formative assessments were implemented and when I utilized information from the formative assessments …

Algebra In The Fifth Grade Mathematics Program, Kathy Bohac

Action Research Projects

In this action research study of my classroom of fifth grade students, I investigated the incorporation of more algebraic concepts in their mathematics curriculum. Due to the restructuring of mathematics courses at the secondary level, my district has suggested that more algebraic concepts be included in the intermediate elementary mathematics curriculum. I discovered that the fifth grade students were not only capable of, but also enjoyed solving algebra equations. As a result of this research, I plan to continue to use the Hands On Equations program each year to enhance the current mathematics curriculum and to improve the fifth graders‟ …

Improving Achievement And Attitude Through Cooperative Learning In Math Class, Scott Johnsen

Action Research Projects

In this action research study of my classroom of eighth grade mathematics, I investigated the use of cooperative learning groups and whether working in groups changed students’ individual achievement and students’ attitudes toward mathematics. I used my eighth grade class of 13 students along with two different types of group formations: teacher-formed groups and student-formed groups. I discovered that the type of group formation can have an impact on the attitudes of students and how well they work together. I also discovered that there was no real change in students’ achievement, but the longer the group worked together the better …

Oral And Written Communication In Classroom Mathematics, Lindsey Sample

Action Research Projects

In this action research study of my classroom of sixth grade mathematics, I investigated the impact of an increase in student oral and written communication on student level of understanding and student self-confidence. I also investigated the changes in my teaching as I increased opportunities for student oral and written communication of mathematics. While I discovered that student level of understanding was not necessarily increased if written communications were increased, I did find that there seemed to be a rise in student level of self-confidence and understanding throughout the course of the research project due to an increase in oral …

Communication: A Vital Skill Of Mathematics, Lexi Wichelt

Action Research Projects

In this action research study of my classroom of seventh grade mathematics, I investigated the impact of communication in the classroom. I focused on asking more open-ended questions in the hopes that students would engage in mathematical discourse with a focus on correctly using mathematical vocabulary. I also looked at the level of students’ understanding and achievement in mathematics class and the accuracy of students’ assessments of their own understanding when there is a focus on asking and answering open-ended questions. I discovered that students had a better understanding of vocabulary when they were asked more open-ended questions. I also …

Palindromes, Stephanie Fuehrer

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

A palindrome is a word or phrase that reads the same forward and backward, such as the word “level” and the phrase “Madam, I’m Adam.” Numbers whose digits read the same forward and backward are also called palindromes, such as the numbers 22, 1234321, and 2002. Palindromic phrases can also occur in number form, for example the Universal day of Symmetry: 8:02 P.M. on February 20, 2002. If one were to look at the time on a twenty-four hour clock, it would read 20:02; the date can be read as the twentieth day of the second month, which also represents …

The Monty Hall Problem, Brian Johnson

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

In the game show "Let's Make a Deal", host Monty Hall would present a contestant with three doors. Behind one door is a car and behind the other two doors are goats. The contestant picks one door, after which Monty opens one of the other doors, showing a goat. Monty then offers the contestant the opportunity to keep the same door or switch to the other unopened door; the contestant will get to keep whatever is behind that door. Should the contestant switch?

Powers, Marci Ostmeyer

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

Powers, or exponents, give us a convenient, shorthand way to denote that a number is multiplied by itself a given number of times. The number being multiplied is called the base, and the number of times it appears in the product is the power.

Project Based Instruction In A Sixth Grade Mathematics Classroom: A Case Of Roller Coasters, Lori L. Pierce

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

In this action research study of a sixth grade mathematics classroom, I investigated how using project based instruction combined with collaborative learning influenced students’ attitudes and beliefs in learning mathematics. I discovered that using a project based approach to instruction helped the students see connections to math and the real world. They felt that math became something exciting instead of just lessons from a book. I also found that most students preferred to work in small groups because they had come to count on their peers for support. They felt that they were more comfortable asking their peers questions in …

Creating Meaningful Homework And Implementing Homework Presentations To Aid In Mathematics Instruction, Gretchen Long

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

In this action research study of sixth grade mathematics, I investigated the use of meaningful homework and the implementation of presentations and its effect on students’ comprehension of mathematical concepts. I collected data to determine whether the creating of meaningful homework and the implementation of homework presentations would have a positive impact on the students’ understanding of the concepts being taught in class and the reasoning behind assigning homework. The homework was based on the lesson taught during class time. It was grade-level appropriate and contained problems similar to those students completed in class. A pre-research and post-research survey based …

Improving Problem Solving By Improving Reading Skills, Shayne Hite

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

In this study of my fifth grade mathematics class, I investigated how the use of different reading strategies impacted my students’ problem solving. I implemented various reading strategies throughout a three-month time period. Teaching my students to break down story problems, learn the steps in solving them, write their own story problems, create math dictionaries, write story problem webs, and listen to themselves reading problems created more confidence in them and increased the likelihood that they would use these strategies on their own. In this research, it was quite obvious to me through some pre-testing that my students struggled with …

Oral Presentations: Exploring Presentations Of Homework Problems As An Alternative Assessment Tool, Michael Ford

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

In this study of my fifth grade mathematics class, I investigated a method of assessing homework presentations as an alternative means of assessment from the more traditional approach of paper and pencil testing. By changing the number of daily problems assigned in my classroom to include shorter assignments and implementing longer, more difficult story problems, I found that students enjoyed mathematics more and had a deeper understanding of the concepts. Increased retention of material, enhanced abilities to communicate problem solving methods, and improved attitudes were all positive side-effects of this project. As a result of my study, I have changed …

Strengthening Student Understanding By Implementing Rubrics To Provide Effective Feedback, Mindy Fichtner

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

In this action research study of my classroom of sixth grade mathematics, I investigated the impact of rubrics on strengthening students’ mathematical understanding and students’ ability to communicate about problem solving processes. The feedback was given on three daily bell-work problems assigned at the beginning of each class over the previous lesson. I discovered that the use of these rubrics were beneficial to the students and teacher. Once students were given the expectations of the bell-work problems and became comfortable with the rubric, the quality of their work and communication of solutions was higher than before the rubric system was …

Mathematical Communication And Achievement Through Journal Writing, Cathy Schultz

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

In this study, I investigated my classroom of sixth grade mathematic students on how journal writing influences students’ writing and learning and how journal writing influences my mathematics teaching. I discovered that students enjoyed writing in their journals and reading my responses. Students could openly communicate their questions, thoughts, and opinions. They shared with me what it was like for a sixth grade math student. They also pointed out the concepts they understood or the ones that challenged them. Some students stated that the journal writing helped them think harder. As a teacher, reading and responding to their journal writing …

Reading Mathematics, Geri Steinbrink

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

In this study of my sixth grade mathematics class, I investigated how using reading strategies, a structured problem-solving form, and math-infused literature impacted students’ success in solving word problems and building geometric vocabulary. Direct instruction of reading strategies and the use of those reading strategies in a structured problem-solving group increased my students’ confidence in their own abilities to solve word problems. The structured problem-solving form served as a reminder of the strategies and the steps students should use when reading and solving a word problem. Students wrote in their journals that they liked the reading of the “Sir Cumference” …