Open Access. Powered by Scholars. Published by Universities.®
- Institution
- Keyword
-
- Derived set (2)
- Limit point (2)
- Topology (2)
- Aesthetic (1)
- Algebra (1)
-
- Analysis (1)
- Assessment (1)
- Axioms (1)
- CUNY (1)
- Cantor set (1)
- Connectedness (1)
- Continuity (1)
- Delta-epsilon (1)
- Developmental education (1)
- Developmental math (1)
- Elements (1)
- Euclid (1)
- Geometry (1)
- Ideals (1)
- Integration (1)
- Lebesgue integral (1)
- Limit (1)
- Linear programming (1)
- Mathematical story (1)
- Mathematics education (1)
- Open-ended questions (1)
- Parallel postulate; hyperbolic geometry (1)
- Problem-solving (1)
- Pythagorean Theorem (1)
- Remedial education (1)
- Publication
- Publication Type
Articles 1 - 20 of 20
Full-Text Articles in Mathematics
Why Be So Critical? Nineteenth Century Mathematics And The Origins Of Analysis, Janet Heine Barnett
Why Be So Critical? Nineteenth Century Mathematics And The Origins Of Analysis, Janet Heine Barnett
Analysis
No abstract provided.
Henri Lebesgue And The Development Of The Integral Concept, Janet Heine Barnett
Henri Lebesgue And The Development Of The Integral Concept, Janet Heine Barnett
Analysis
No abstract provided.
The Failure Of The Euclidean Parallel Postulate And Distance In Hyperbolic Geometry, Jerry Lodder
The Failure Of The Euclidean Parallel Postulate And Distance In Hyperbolic Geometry, Jerry Lodder
Geometry
No abstract provided.
Richard Dedekind And The Creation Of An Ideal: Early Developments In Ring Theory, Janet Heine Barnett
Richard Dedekind And The Creation Of An Ideal: Early Developments In Ring Theory, Janet Heine Barnett
Abstract Algebra
No abstract provided.
The Remedy That's Killing: Cuny, Laguardia, And The Fight For Better Math Policy, Rachel A. Oppenheimer
The Remedy That's Killing: Cuny, Laguardia, And The Fight For Better Math Policy, Rachel A. Oppenheimer
Dissertations, Theses, and Capstone Projects
Nationwide, there is a crisis in math learning and math achievement at all levels of education. Upwards of 80% of students who enter the City University of New York’s community colleges from New York City’s Department of Education high schools fail to meet college level math proficiencies and as a result, are funneled into the system’s remedial math system. Once placed into pre-college remedial arithmetic, pre-algebra, and elementary algebra courses, students fail at alarming rates and research indicates that students’ failure in remedial math has negative ripple effects on their persistence and degree completion. CUNY is not alone in facing …
The Cantor Set Before Cantor, Nicholas A. Scoville
The Cantor Set Before Cantor, Nicholas A. Scoville
Topology
A special construction used in both analysis and topology today is known as the Cantor set. Cantor used this set in a paper in the 1880s. Yet it appeared as early as 1875 in a paper by the Irish mathematician Henry John Stephen Smith (1826 - 1883). Smith, who is best known for the Smith normal form of a matrix, was a professor at Oxford who made great contributions in matrix theory and number theory. In this project, we will explore parts of a paper he wrote titled On the Integration of Discontinuous Functions.
Topology From Analysis, Nicholas A. Scoville
Topology From Analysis, Nicholas A. Scoville
Topology
Topology is often described as having no notion of distance, but a notion of nearness. How can such a thing be possible? Isn't this just a distinction without a difference? In this project, we will discover the notion of nearness without distance by studying the work of Georg Cantor and a problem he was investigating involving Fourier series. We will see that it is the relationship of points to each other, and not their distances per se, that is a proper view. We will see the roots of topology organically springing from analysis.
Connecting Connectedness, Nicholas A. Scoville
The Exigency Of The Euclidean Parallel Postulate And The Pythagorean Theorem, Jerry Lodder
The Exigency Of The Euclidean Parallel Postulate And The Pythagorean Theorem, Jerry Lodder
Geometry
No abstract provided.
Using Ipads And Video-Based Instruction To Teach Algebra To High School Students With Disabilities, Elias Clinton, Tom J. Clees
Using Ipads And Video-Based Instruction To Teach Algebra To High School Students With Disabilities, Elias Clinton, Tom J. Clees
National Youth Advocacy and Resilience Conference
This presentation targets a study in which four high school students with disabilities were taught to solve algebraic equations using iPads and video-based instruction. All students showed immediate increases in accurate responding following the introduction of the video-based intervention. This presentation provides practitioners with a flexible technology-based intervention for students with disabilities in need of grade-level academic instruction. The intervention could be used across a variety of subjects and academic tasks.
Session E-2: Function Fundamentals, More Than X And Y, Carlo Ordonez, Steven M. Condie
Session E-2: Function Fundamentals, More Than X And Y, Carlo Ordonez, Steven M. Condie
Professional Learning Day
How many of your students say that √9 = ±3? This may have to do with a lack of understanding of functions. This session will highlight some of the nuances of functions with less formal, non-formula driven examples with which students can expand their understanding.
Session F-4: Developing Parametric Equations Using Mathematical Modeling, Mark Kammrath
Session F-4: Developing Parametric Equations Using Mathematical Modeling, Mark Kammrath
Professional Learning Day
Designing project to develop student understanding of parametric equations and two modeling situations in which they are applied. No previous knowledge of parametrics is required by the students. The project requires two days of class time, with the remaining work done outside of class. This project is intended to be given three days into a unit on vectors.
Session F-1: Exploration Geometry: Hands-On Transformations, Lindsey Herlehy, David Hernandez, Karen Togliatti
Session F-1: Exploration Geometry: Hands-On Transformations, Lindsey Herlehy, David Hernandez, Karen Togliatti
Professional Learning Day
In this session, participants will engage in a series of hands-on, minds-on Geometry lessons designed to explore the four transformations. By completing several critical thinking challenges, teachers will use the Common Core Mathematical Practices and various manipulatives to investigate how figures rotate, dilate, translate, and reflect within a plane. Appropriate for multiple grade levels, teachers will leave the session with all instructional plans and various ways to adapt the lesson based on the needs of their students.
Session D-3: The Mathematical Wonders Of Pascal's Triangle, Donald Porzio
Session D-3: The Mathematical Wonders Of Pascal's Triangle, Donald Porzio
Professional Learning Day
Most mathematics teachers are aware of the some of the more straightforward connections Pascal's Triangle has to mathematics. Come explore some of the lesser known connections that can be used to peak your students' interest and entice them into exploring the mathematics behind these connections.
Session A-4: It’S A Wrap, Lindsey Herlehy, David Hernandez
Session A-4: It’S A Wrap, Lindsey Herlehy, David Hernandez
Professional Learning Day
Investigate the concepts of surface area, measurement, ratio and proportion through a visual and kinesthetic mathematical investigation. Participants will be presented with the challenge of calculating how many sheets of toilet paper it would take to wrap one of their group members using a limited selection of tools. This session will provide teachers with a wonderful hands-on, minds-on activity that could easily be implemented into any classroom!
Session A-3: The Box Problem – An Introduction, Ruth Dover
Session A-3: The Box Problem – An Introduction, Ruth Dover
Professional Learning Day
Create some simple boxes with paper and scissors. Then we'll measure the height, area of the base, and the volume. Find formulas, find regressions, and graph the functions. It's a simple activity to engage students and combine many different aspects of mathematics.
Session C-2: “It Is Easy As Pi”, Christine L. Moskalik, Carmela Jones
Session C-2: “It Is Easy As Pi”, Christine L. Moskalik, Carmela Jones
Professional Learning Day
Participants will work together using pi to try to open an ancient chest filled with treasure!! The chest is protected by a passcode that can only be determined through the activities within the lesson. Enjoy a progressive exposure to pi through this two-part lesson (total 110 minutes) offering a FUN storyline within the context of geometry and circles. With "pi-day" right around the corner, this hands-on, fun, inquiry-based lesson is sure to be a hit with your budding mathematicians.
Knowledge And Tasks Connecting Elementary, Secondary, And Disciplinary Mathematics, Yvonne Lai
Knowledge And Tasks Connecting Elementary, Secondary, And Disciplinary Mathematics, Yvonne Lai
DBER Speaker Series
A well-prepared teacher should be able to help her students see mathematics as ideas that develop over time. Mathematics courses designed specifically for prospective secondary teachers aim for prospective teachers to see and find connections across elementary, secondary, and disciplinary mathematics, and beyond that to be able to use those connections in their future teaching. While there is broad agreement with these aims, there is also little consensus around how to carry them out. Two challenges in meeting these aims are identifying content that lends itself to such connections and designing tasks that can be used to engage with that …
The Role Of Sequence In The Experience Of Mathematical Beauty, Leslie Dietiker
The Role Of Sequence In The Experience Of Mathematical Beauty, Leslie Dietiker
Journal of Humanistic Mathematics
In this article, I analyze the aesthetic dimensions of a sequence of mathematical events found in an unusual first grade lesson in order to demonstrate how sequencing may affect an individual’s experience of mathematical beauty. By approaching aesthetic as a sense or felt quality of an experience in context (Sinclair, 2001, 2011), this analysis explains how sequence can affect the way mathematical objects or actions are experienced by an individual. Thus, rather than questioning whether or in what ways a set of mathematical objects are beautiful or not, this paper addresses under what conditions is the mathematics in play beautiful. …
Multiple Problem-Solving Strategies Provide Insight Into Students’ Understanding Of Open-Ended Linear Programming Problems, Marla A. Sole
Multiple Problem-Solving Strategies Provide Insight Into Students’ Understanding Of Open-Ended Linear Programming Problems, Marla A. Sole
Publications and Research
Open-ended questions that can be solved using different strategies help students learn and integrate content, and provide teachers with greater insights into students’ unique capabilities and levels of understanding. This article provides a problem that was modified to allow for multiple approaches. Students tended to employ high-powered, complex, familiar solution strategies rather than simpler, more intuitive strategies, which suggests that students might need more experience working with informal solution methods. During the semester, by incorporating open-ended questions, I gained valuable feedback, was able to better model real-world problems, challenge students with different abilities, and strengthen students’ problem solving skills.