Science and Mathematics Education Commons^™

Reasonable Or Not? A Study Of The Use Of Teacher Questioning To Promote Reasonable Mathematical Answers From Sixth Grade Students, Marlene Grayer

Action Research Projects

In this action research study of my sixth grade mathematics class, I investigated the influence a change in my questioning tactics would have on students’ ability to determine answer reasonability to mathematics problems. During the course of my research, students were asked to explain their problem solving and solutions. Students, amongst themselves, discussed solutions given by their peers and the reasonability of those solutions. They also completed daily questionnaires that inquired about my questioning practices, and 10 students were randomly chosen to be interviewed regarding their problem solving strategies. I discovered that by placing more emphasis on the process rather …

The Role Of Manipulatives In The Eighth Grade Mathematics Classroom, Michaela Ann Goracke

Action Research Projects

In this action research study of my classroom of eighth grade mathematics, I investigated the use of manipulatives and its impact on student attitude and understanding. I discovered that overall, students enjoy using manipulatives, not necessarily for the benefit of learning, but because it actively engages them in each lesson. I also found that students did perform better on exams when students were asked to solve problems using manipulatives in place of formal written representations of situations. In the course of this investigation, I also uncovered that student attitude toward mathematics improved when greater manipulative use was infused into the …

Writing In Math Class? Written Communication In The Mathematics Classroom, Stephanie Fuehrer

Action Research Projects

In this action research study of my seventh grade mathematics classroom, I investigated what written communication within the mathematics classroom would look like. I increased vocabulary instruction of specific mathematical terms for my students to use in their writing. I also looked at what I would have to do differently in my teaching in order for my students to be successful in their writing. Although my students said that using writing to explain mathematics helped them to better understand the math, my research revealed that student writing did not necessarily translate to improved scores. After direct instruction and practice on …

Holding Students Accountable, Jeremy Fries

Action Research Projects

This action research study of approximately 90 high school algebra students investigates how frequent quizzing benefits them during the course of a semester. The intent of the research was to see how well students kept up with the material and if frequent quizzing helped them on the chapter tests. It was also designed to help me gain a better understanding of what students know and how I need to adjust daily routines so that all students stay caught up. I discovered that although frequent quizzes are not the students’ favorite activity to take part in, they learn to accept the …

Palindromes, Stephanie Fuehrer

Department of Mathematics: Master 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 …

Sudoku, Marlene Grayer

Department of Mathematics: Master 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 …

The Monty Hall Problem, Brian Johnson

Department of Mathematics: Master 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?

Advisor: Gordon Woodward

Powers, Marci Ostmeyer

Department of Mathematics: Master 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.

Amicable Pairs, Lexi Wichelt

Department of Mathematics: Master 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.

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

Department of Teaching, Learning, and Teacher Education: Master 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 …

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

Department of Teaching, Learning, and Teacher Education: Master 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 …

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

Department of Teaching, Learning, and Teacher Education: Master 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

Department of Teaching, Learning, and Teacher Education: Master 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 …

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

Department of Teaching, Learning, and Teacher Education: Master 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 …

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

Department of Teaching, Learning, and Teacher Education: Master 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 …

Reading Mathematics, Geri Steinbrink

Department of Teaching, Learning, and Teacher Education: Master 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” …

Grades 3-5 Pollution, Amy Silviotti

Science

This is a science lesson for grades third through five on pollution. Through this lesson students will be able to describe the relationships among air, water, land on Earth, characteristics of living and non living things, survival behaviors of common living specimens, the factors that help promote good health. Students will also be able to identify how plants and animals depend on each other and in what ways humans have changed the environment. The lesson is tiered in three levels based on ability. Within each tier the student will complete a shape contract where they choose tasks based on interest …

Modeling And Analysis Of Biological Populations, Joan Lubben

Department of Mathematics: Dissertations, Theses, and Student Research

Asymptotic and transient dynamics are both important when considering the future population trajectory of a species. Asymptotic dynamics are often used to determine whether the long-term trend results in a stable, declining or increasing population and even provide possible directions for management actions. Transient dynamics are important for estimating invasion speed of non-indigenous species, population establishment after releasing biocontrol agents, or population management after a disturbance like fire. We briefly describe here the results in this thesis.

(1) We consider asymptotic dynamics using discrete time linear population models of the form n(t + 1) = An(t) where …

Fan Cohomology And Its Application To Equivariant K-Theory Of Toric Varieties, Suanne Au

Department of Mathematics: Dissertations, Theses, and Student Research

Mu-Wan Huang, Mark Walker and I established an explicit formula for the equivariant K-groups of affine toric varieties. We also recovered a result due to Vezzosi and Vistoli, which expresses the equivariant K-groups of a smooth toric variety in terms of the K-groups of its maximal open affine toric subvarieties. This dissertation investigates the situation when the toric variety X is neither affine nor smooth. In many cases, we compute the Čech cohomology groups of the presheaf K_q^T on X endowed with a topology. Using these calculations and Walker's Localization Theorem for equivariant K-theory, we give explicit formulas …

Concept Booklets: Examining The Performance Effects Of Journaling Of Mathematics Course Concepts, Todd Stephen Fogdall

Boise State University Theses and Dissertations

Journaling is an effective tool for writing about mathematics, but research is mixed about the extent to its effectiveness in writing to learn mathematics. This study examined the performance effects of concept booklets on curriculum assessments. Concept booklets are a hybrid style of journal-writing that include responses to journal prompts, diagramming, and traditional note-taking. Prompts were designed to sometimes investigate new concepts and, at other times, to reflect on components of previously learned concepts.

The study, of an experimental design, was carried out at the high school level in honors-level mathematics classes with the independent variable being exposure to the …

Parts Of The Whole: Approaching Education As A System, Dorothy Wallace

Numeracy

An educational system is a highly coupled complex system of inputs, outputs, sensors and actuators. Using an engineering perspective, this column begins the process of naming and categorizing parts of the system. It then focuses on teachers as one part of a large system, and analyzes the forces that influence how teachers work, and that draw or repel individuals to a teaching career. The growing shortage of qualified teachers can be explained by properties of the system as a whole that determine the context in which teachers do their job.

Review Of Super Crunchers By Ian Ayers, Eric Gaze

Numeracy

Ayers, I. Super Crunchers: Why Thinking-by-Numbers Is the New Way to be Smart. (Bantam Dell Publishing Group, 2007). 272 pp. Hard cover $25 ISBN 978-0-553-80540-6.

Super Crunchers tells the story of how analyzing data is changing the ways in which decisions are made. We in the National Numeracy Network make a case for the importance of quantitative literacy by referring to how much quantitative information is now available to each of us: “a world awash in numbers.” Ian Ayres zeroes in on the people who are making a living crunching all of these data. From the seemingly innocuous (how …

Review Of Stat-Spotting: A Field Guide To Identifying Dubious Data By Joel Best, Joe Swingle

Numeracy

Best, Joel. Stat-Spotting: A Field Guide to Identifying Dubious Data. (Berkeley: University of California Press, 2008) 144 pp. $19.95. ISBN 1-978-0-520-25746-7.

Stat-Spotting is a practical, do-it-yourself manual for detecting questionable claims reported in the media. Using examples drawn mostly from mass media sources, Stat-Spotting provides readers with a number of useful tips for identifying potentially problematic statistics. The author’s skillful analyses and explanations presented in clear and concise prose make Stat-Spotting an ideal guide for anyone who reads a newspaper, watches television, or surfs the Web. In short, everyone.

Review Of Calculation Vs. Context: Quantitative Literacy And Its Implications For Teacher Education By Bernard L. Madison And Lynn Arthur Steen (Editors), Maura B. Mast

Numeracy

Madison, Bernard L. and Steen, Lynn Arthur (Eds.). Calculation vs. Context: Quantitative Literacy and Its Implications for Teacher Education. (Washington, DC: Mathematical Association of America, 2009). 197 pp. Softcover. ISBN 978-0-88385-908-7. Available free on the MAA website at http://www.maa.org/ql/calcvscontext.html

The papers in Calculation vs. Context discuss the role of quantitative literacy in the K-12 curriculum and in teacher education. The papers present a varied set of perspectives and address three themes: the changing environment of education in American society; the challenges, and the necessity, of preparing teachers to teach quantitative literacy and of including quantitative literacy in the K-12 education; …

Engaging Math-Avoidant College Students, M. Paul Latiolais, Wendi Laurence

Numeracy

This paper is an informal, personal account of how we, as two college teachers, became interested in math anxiety, decided to explore it amongst students at our institution in order to inform our teaching, and became convinced that the massive problem is math avoidance. We tried discussion groups, but few students attended, although those that did made useful suggestions. Thus informed, we designed an innovative course, Confronting College Mathematics as a Humanities course with the possibility of credit toward the math requirement, but it was undersubscribed in its first offering and had to be canceled. How can we get college …

Measuring Resource Inequality: The Gini Coefficient, Michael T. Catalano, Tanya L. Leise, Thomas J. Pfaff

Numeracy

This paper stems from work done by the authors at the Mathematics for Social Justice Workshop held in June of 2007 at Middlebury College. We provide a description of the Gini coefficient and some discussion of how it can be used to promote quantitative literacy skills in mathematics courses. The Gini Coefficient was introduced in 1921 by Italian statistician Corrado Gini as a measure of inequality. It is defined as twice the area between two curves. One, the Lorenz curve for a given population with respect to a given resource, represents the cumulative percentage of the resource as a function …

Quantitative Literacy Assessments: An Introduction To Testing Tests, Dorothy Wallace, Kim Rheinlander, Steven Woloshin, Lisa Schwartz

Numeracy

This paper describes how professional evaluators construct assessment instruments that work properly to measure the right thing. Constructing an assessment tool begins with getting feedback from relevant experts on the content of questions. The tool is developed and refined through comparison with existing instruments, focus groups and cognitive interviews. The final instrument is formally tested for content validity, usability, reliability and construct validity through a variety of statistical measures. This process of construction is illustrated by two examples relevant to quantitative literacy: the Medical Data Interpretation Test and the Math Attitudes Survey.

Integration With Writing Programs: A Strategy For Quantitative Reasoning Program Development, Nathan D. Grawe, Carol A. Rutz

Numeracy

As an inherently interdisciplinary endeavor, quantitative reasoning (QR) risks falling through the cracks between the traditional “silos” of higher education. This article describes one strategy for developing a truly cross-campus QR initiative: leverage the existing structures of campus writing programs by placing QR in the context of argument. We first describe the integration of Carleton College’s Quantitative Inquiry, Reasoning, and Knowledge initiative with the Writing Program. Based on our experience, we argue that such an approach leads to four benefits: it reflects important aspects of QR often overlooked by other approaches; it defuses the commonly raised objection that QR is …

Assessing Quantitative Reasoning, Corrine H. Taylor

Numeracy

No abstract provided.

The Influence Of Risk Taking On Student Creation Of Mathematical Meaning: Contextual Risk Theory, Erin Nicole Houghtaling

Theses and Dissertations

The primary concerns of mathematics educators are learning and teaching mathematics. It is, therefore, natural to ask "what implications and benefits might there be if learning were perceived as a risk-taking event?" (Atkinson, 1957, p. 266). The underlying motivation of this study is to analyze the risks students take in the mathematics classroom and how risk influences student creation of meaning and development of understanding. I define risk in the mathematics classroom to be any observable act that entails uncertain outcome. The research presented here focuses on a table of four students: Andrew, Carina, Kam, and Mark as they grapple …