Quantitative Reasoning In The Contemporary World, 2: Focus Questions For The Numeracy Community,
2010
University of Arkansas
Quantitative Reasoning In The Contemporary World, 2: Focus Questions For The Numeracy Community, Bernard L. Madison, Shannon W. Dingman
Numeracy
Numerous questions about student learning of quantitative reasoning arose as we developed, taught and assessed the Quantitative Reasoning in the Contemporary World course described in the companion paper in this issue of Numeracy. In this paper, we present some of those questions and describe the context in which they arose. They fall into eight general problem areas: learning that is context-bound and does not easily transfer (i.e., situated learning); the need for a productive disposition regarding mathematics; the connection between QL and mathematical proficiency; the persistence of students, despite our efforts, for using the wrong base for percents; the inconsistent …
Quantitative Reasoning In The Contemporary World, 1: The Course And Its Challenges:,
2010
University of Arkansas - Main Campus
Quantitative Reasoning In The Contemporary World, 1: The Course And Its Challenges:, Shannon W. Dingman, Bernard L. Madison
Numeracy
The authors describe successes and challenges in developing a QL-friendly course at the University of Arkansas. This work is part of a three-year NSF project Quantitative Reasoning in the Contemporary World (QRCW) that supported the expansion of the course. The course, MATH 2183, began experimentally in Fall 2004 as a section of finite mathematics known informally as “News Math” for 26 students from arts and humanities disciplines. Over the past six years, the course has evolved and now MATH 2183 is approved to satisfy the College of Arts and Sciences mathematics requirement for the Bachelor of Arts degree. In 2009-2010, …
Quantitative Literacy: Does It Work? Evaluation Of Student Outcomes At Colby-Sawyer College,
2010
Colby-Sawyer College
Quantitative Literacy: Does It Work? Evaluation Of Student Outcomes At Colby-Sawyer College, Benjamin Steele, Semra Kilic-Bahi
Numeracy
Colby-Sawyer College has adopted a mission for quantitative literacy (QL) to give students the “necessary skills to understand and use quantitative information in their personal and professional lives.” We have implemented an across-the-curriculum approach to develop these skills. As part of this QL program, we administer two assessment tests, one in basic mathematical skills and one that applies those skills, plus an attitude survey to both freshmen and seniors. Three years of data show that seniors score about 10 percentage points higher than freshmen on these tests. However, seniors still scored below 55 percent on both tests, and many cannot …
Advancing Assessment Of Quantitative And Scientific Reasoning,
2010
James Madison University
Advancing Assessment Of Quantitative And Scientific Reasoning, Donna L. Sundre, Amy D. Thelk
Numeracy
Advancing Assessment of Quantitative and Scientific Reasoning is a four-year NSF Project (DUE-0618599) in part designed to evaluate the generalizability of quantitative (QR) and scientific reasoning (SR) assessment instruments created at James Madison University to four other four-year institutions with very distinct missions and student demographics. This article describes the methods, results, and findings we obtained in our studies. More specifically, we describe how to conduct content-alignment exercises in which faculty members map each item from a prospective test to the student learning objectives taught at the institution. Our results indicated that 92-100% of the QR and SR items were …
Science Literacy: Hand In Glove With Numeracy,
2010
University of South Florida, Tampa
Science Literacy: Hand In Glove With Numeracy, Gerry G. Meisels
Numeracy
Science Literacy requires numeracy as part of its foundation, and much of Numeracy draws on examples and applications from the sciences. They share the goal of creating a society that is mathematics numerate and science literate, and are interrelated. National priorities to strengthen both among all our students are driven by practical considerations of economic competitiveness that increasingly depend on technological innovation. It is also critical to each individual for long-term job opportunities and for informed citizenship. With up to 80% of 21st century jobs requiring mathematics and science skills, a large majority of the 2,900,000 students who graduate from …
Extension Of Plurisubharmonic Functions With Growth Control,
2010
Syracuse University
Extension Of Plurisubharmonic Functions With Growth Control, Dan Coman, Vincent Guedj, Ahmed Zeriahi
Mathematics - All Scholarship
Suppose that X is an analytic subvariety of a Stein manifold M and that varphi is a plurisubharmonic (psh) function on X which is dominated by a continuous psh exhaustion function u of M. Given any number c > 1, we show that varphi admits a psh extension to M which is dominated by cu on M. We use this result to prove that any omega-psh function on a subvariety of the complex projective space is the restriction of a global omega-psh function, where omega is the Fubini-Study Kahler form.
Rules Without Reason: Allowing Students To Rethink Previous Conceptions,
2010
University of Montana
Rules Without Reason: Allowing Students To Rethink Previous Conceptions, Mary Mueller, Dina Yankelewitz, Carolyn Maher
The Mathematics Enthusiast
This paper reports on the strategies chosen by a group of sixth-grade students in an urban informal learning program as they worked to solve an open-ended, nonroutine task. In particular, the paper focuses on the ability of these students to rise above their previous, procedure-based misconceptions and arrive at a mathematically reasonable solution. Aspects of the problem task, the problem-solving environment, and, importantly, of the nature of the teacher’s interventions are analyzed to determine the conditions that encouraged students to approach mathematics as a logical, meaningful, sense-making activity.
Climbing And Angles: A Study Of How Two Teachers Internalize And Implement The Intentions Of A Teaching Experiment,
2010
University of Montana
Climbing And Angles: A Study Of How Two Teachers Internalize And Implement The Intentions Of A Teaching Experiment, Anne Birgitte Fyhn
The Mathematics Enthusiast
In this innovative teaching experiment, the context of climbing is used to induce the teaching and learning of angle concepts. This article reports on the outcomes of a three day teaching and climbing experiment and the impact of this experience on the teacher’s understanding of meso and micro embodiments of mathematics, angle representations, as well as shifts in their attitudes about teaching/learning geometry.
Rehearsal Or Reorganization: Two Patterns Of Literacy Strategy Use In Secondary Mathematics Classes,
2010
University of Montana
Rehearsal Or Reorganization: Two Patterns Of Literacy Strategy Use In Secondary Mathematics Classes, Anne Adams
The Mathematics Enthusiast
This study presents two critical cases illustrating distinct patterns in teachers' use of literacy strategies in secondary mathematics classes. The cases are part of a professional development project designed to enhance teachers' pedagogical skills by developing content literacy strategies for use in secondary mathematics and science classrooms. Teachers' beliefs about teaching mathematics, their uses of writing and vocabulary development strategies, and goals for student learning were examined via interviews, classroom observations, reflections on teaching, and teacher posts to an online discussion forum. Results show patterns of literacy strategy use were related to teachers' views of pedagogy and of mathematics. Ned, …
Population Models With Allee Effect: A New Model,
2010
Trinity University
Population Models With Allee Effect: A New Model, Saber Elaydi, Robert J. Sacker
Mathematics Faculty Research
In this paper we develop several mathematical models of Allee effects. We start by defining the Allee effect as a phenomenon in which individual fitness increases with increasing density. Based on this biological assumption, we develop several fitness functions that produce corresponding models with Allee effects. In particular, a rational fitness function yields a new mathematical model that is our focus of study. Then we study the dynamics of 2-periodic systems with Allee effects and show the existence of an asymptotically stable 2-periodic carrying capacity.
Cultural Conflicts In Mathematics Classrooms And Resolution: The Case Of Immigrants From The Former Soviet Union And Israeli "Old Timers",
2010
University of Montana
Cultural Conflicts In Mathematics Classrooms And Resolution: The Case Of Immigrants From The Former Soviet Union And Israeli "Old Timers", Miriam Amit
The Mathematics Enthusiast
This paper describes a singular process that has been transforming mathematics education in Israel over the past 20 years, as a result of a massive influx of mathematics teachers from the former Soviet Union (FSU). It traces the key points of conflict that marked the initial contact between Israel's mathematical and educational culture and the codes and values brought with the immigrant teachers from the FSU. It then shows how this conflict is gradually becoming resolved, as the two disparate cultures merge into a single, new culture, based on 'the best of both worlds.' This case, we claim, can serve …
Some Reflections On Hernández And López’S Reflections On The Chain Rule,
2010
University of Montana
Some Reflections On Hernández And López’S Reflections On The Chain Rule, Michael N. Fried
The Mathematics Enthusiast
To shed light on how history of mathematics can play a role in mathematics education, Hernández and López chose well in focusing on the chain rule as a case study. Generally speaking, it is, as they point out, a topic students find difficult to grasp: it is a rule involving a different order of complexity than, say, the rule for differentiating functions of the form f(x)=xn, and, although it can eventually become intuitive, it is far from intuitive at the start. Harel et al. (2009) have pointed out that students’ difficulties with the chain rule involve: “...coordinating three or more …
Magic Circles In The Arbelos,
2010
University of Montana
Magic Circles In The Arbelos, Christer Bergsten
The Mathematics Enthusiast
In the arbelos three simple circles are constructed on which the tangency points for three circle chains, all with Archimedes’ circle as a common starting point, are situated. In relation to this setting, some algebraic formulae and remarks are presented. The development of the ideas and the relations that were “discovered” were strongly mediated by the use of dynamic geometry software.
Vectors In Climbing,
2010
University of Montana
Vectors In Climbing, Anne Birgitte Fyhn
The Mathematics Enthusiast
In this article, the work on mesospace embodiments of mathematics is further developed by exploring the teaching and learning of vector concepts through climbing activities. The relevance and connection between climbing and vector algebra notions is illustrated via embedded digital videos.
The History Of Mathematics As A Pedagogical Tool: Teaching The Integral Of The Secant Via Mercator’S Projection,
2010
The University of Montana
The History Of Mathematics As A Pedagogical Tool: Teaching The Integral Of The Secant Via Mercator’S Projection, Nick Haverhals, Matt Roscoe
The Mathematics Enthusiast
This article explores the use of the history of mathematics as a pedagogical tool for the teaching and learning of mathematics. In particular, we draw on the mathematically pedigreed but misunderstood development of the Mercator projection and its connection to the integral of the secant function. We discuss the merits and the possible pitfalls of this approach based on a teaching module with undergraduate students. The appendices contain activities that can be implemented as an enrichment activity in a Calculus course.
Problem Posing From The Foundations Of Mathematics,
2010
University of Montana
Problem Posing From The Foundations Of Mathematics, Libby Knott
The Mathematics Enthusiast
This reflective paper develops a repertoire of questions for teachers to use in their classrooms during episodes of mathematics discussions with and among students. These questions are motivated by an examination of questions posed by Wittgenstein in Zettel, and are connected to underlying tacit assumptions about mathematics, most of which lie subtly below the generally accepted milieu of math-talk. Once classrooms norms have been established to encourage participation by all students in a democratic and just classroom environment, these questions can be used effectively to stimulate meaningful discourse. These questions provide important examples of problem posing designed to encourage student …
A Semiotic Reflection On The Didactics Of The Chain Rule,
2010
University of Montana
A Semiotic Reflection On The Didactics Of The Chain Rule, Omar Hernandez Rodriguez, Jorge M. Lopez Fernandez
The Mathematics Enthusiast
According to (Fried, 2008), there is an intrinsic tension in trying to apply the history of mathematics to its didactics. Besides the widespread feeling that the introduction of didactic elements taken from the history of mathematics can detract the pedagogy of mathematics from the attainment of important goals, (Fried, 2008, p. 193) describes a pair of specific pitfalls that can arise in implementing such historical applications in mathematics education. The description in (Fried, 2008), is presented in the parlance of Sausserian Semiotics and identifies two semiotic “deformations” that arise when one fails to observe that the pairing between signs and …
The Influence Of A Multidisciplinary Scientific Research Experience On Teachers Views Of Nature Of Science,
2010
University of Montana
The Influence Of A Multidisciplinary Scientific Research Experience On Teachers Views Of Nature Of Science, Jerine Pegg, Edith Gummer
The Mathematics Enthusiast
This study examined a professional development project for K-12 science teachers that engaged participants in an authentic scientific investigation along with explicit-reflective attention to nature of science (NOS). The Views of Nature of Science (VNOS) and Views of Scientific Inquiry (VOSI) Questionnaires (Lederman, Abd-El-Khalick, Bell, & Schwartz, 2002; Schwartz, Lederman, & Thompson, 2001) were used to examine the relationship between teachers’ views of NOS and specific aspects of the professional development project. Results of the study show that teachers’ views of NOS were influenced by the multidisciplinary, primarily non-experimental research that they engaged in, the opportunity to observe interactions of …
Epilogue,
2010
University of Montana
Epilogue, Bharath Sriraman
The Mathematics Enthusiast
The table of contents of this double issue included the above quote from the historian Howard Zinn which might seem puzzling to the reader. Why was this quote included and what is it supposed to mean? In the opening editorial, I mused over the whole enterprise of scholarly publishing and what it amounts to in the grand scheme of things. Zinn’s quote reminds us that academia is a cloistered unit and many of the things we place importance on in the academic culture of publish or perish seem insignificant when viewed through the lens of real problems that occur outside …
So Many Journals, So Many Words... So What?,
2010
University of Montana
So Many Journals, So Many Words... So What?, Bharath Sriraman
The Mathematics Enthusiast
No abstract provided.
