Graph Theoretical Modeling of DNA as a Vehicle for a Course-Based Undergraduate Research Experience

This paper outlines a mathematics course centered around the interdisciplinary topic of modeling self-assembling DNA which was used as a venue for a mathematics course-based undergraduate research experience (CURE). The structure and logistics of designing and teaching such a course in addition to suggestions and student feedback from the course are also included

Comparing Mastery-based Testing with Traditional Testing in Calculus II

The authors present the results of quantitative data and student feedback from a two-year study of the effects of a new assessment model called “mastery-based testing.” In mastery-based testing, students are given problems in which they can only receive full credit for the problem after they demonstrate mastery of the objective being assessed. This method strives to increase complete understanding of concepts through a growth-mindset approach to learning in addition to helping alleviate math anxiety. In this study, we compare the impact of mastery-based testing with traditional testing in six Calculus II classes. The data sources for the project included end-of-semester surveys, a final mastery assessment, and end-of-semester course grades. We found that mastery-based testing led to students feeling the assessments better reflected their content knowledge as well as higher end-of-semester course grades with fewer hours spent studying outside of class

The Impact of Math Teachers’ Circles on Teacher Dispositions toward Inquiry-based Learning: A Comparison between a Three-day and a One-day Summer Workshop

High-quality professional development for K-12 teachers is a critical need for both teachers and their students. For teachers to provide more engaging and powerful learning opportunities for their students, researchers suggest that we provide similar opportunities for teachers. That is, professional development should model high-impact instructional strategies. Math Teachers\u27 Circles provide one such model for this type of training. In this paper, we discuss the impact on participants of a one-day and participants of a three-day Math Teachers\u27 Circle workshop. In particular, we compare how teacher dispositions regarding the teaching of mathematics and inquiry-based learning changed between the workshops

Analyzing the Impact of Active Learning in General Education Mathematics Courses

This talk shares the preliminary results of a study that explores the general perceptions and attitudes of students in general education mathematics courses taught using primarily active learning- based methods (like group work, projects, and discovery learning), and compares them with those enrolled in a general education mathematics course taught in a more traditional and lecture-based method. We present an analysis of survey data collected throughout the semester, which explores the disposition and mindset of students, their mathematical confidence and anxiety, and perceptions of pedagogical methods used for the teaching of mathematics. We also explored how these perceptions and dispositions changed throughout the course by comparing pre, mid, and post surveys

Locally compact property A groups

Indiana University-Purdue University Indianapolis (IUPUI)In 1970, Serge Novikov made a statement which is now called, "The Novikov Conjecture" and is considered to be one of the major open problems in topology. This statement was motivated by the endeavor to understand manifolds of arbitrary dimensions by relating the surgery map with the homology of the fundamental group of the manifold, which becomes diffi cult for manifolds of dimension greater than two. The Novikov Conjecture is interesting because it comes up in problems in many different branches of mathematics like algebra, analysis, K-theory, differential geometry, operator algebras and representation theory. Yu later proved the Novikov Conjecture holds for all closed manifolds with discrete fundamental groups that are coarsely embeddable into a Hilbert space. The class of groups that are uniformly embeddable into Hilbert Spaces includes groups of Property A which were introduced by Yu. In fact, Property A is generally a property of metric spaces and is stable under quasi-isometry. In this thesis, a new version of Yu's Property A in the case of locally compact groups is introduced. This new notion of Property A coincides with Yu's Property A in the case of discrete groups, but is different in the case of general locally compact groups. In particular, Gromov's locally compact hyperbolic groups is of Property A

Optimal Tile-Based DNA Self-Assembly Designs for Lattice Graphs and Platonic Solids

A design goal in self-assembly of DNA nanostructures is to find minimal sets of branched junction molecules that will self-assemble into targeted structures. This process can be modeled using techniques from graph theory. This paper is a collection of proofs for a set of DNA complexes which can be represented by specific graphs, namely Platonic solids, square lattice graphs, and triangular lattice graphs. This work supplements the results presented in https://arxiv.org/abs/2108.0003

Start a Math Teacher Circle: Connect K-12 Teachers with Engaging, Approachable, and Meaningful Mathematical Problems

Many K-12 math teachers are not ready to teach from a conceptual and inquiry-oriented perspective because they have an algorithmic understanding of mathematics. One solution is to create a math teacher circle (MTC), which provides conceptual and inquiry-based learning activities and builds professionalism among the teachers. In this paper, we describe the origins of two such MTCs, highlighting the process of identifying leadership team members, submitting the grant proposal for seed money, and hosting launch events, intensive summer workshops, and monthly meetings during the academic year. We also share opportunities for professional development for college and university faculty, including research linked to shifts in in-service teacher attitudes. We finish the paper with several of this year’s best activities used at our MTC meetings, including fair division, extensions and generalizations of numerical and algebraic patterns, and applications in cryptography

Start a Math Teacher Circle: Connect K-12 Teachers with Engaging, Approachable, and Meaningful Mahtematical Problems

Many K-12 math teachers are not ready to teach from a conceptual and inquiry-oriented pe

Optimal Tilings of Bipartite Graphs Using Self-Assembling DNA

Motivated by the recent advancements in nanotechnology and the discovery of new laboratory techniques using the Watson-Crick complementary properties of DNA strands, formal graph theory has recently become useful in the study of self-assembling DNA complexes. Construction methods based on graph theory have resulted in significantly increased efficiency. We present the results of applying graph theoretical and linear algebra techniques for constructing crossed-prism graphs, crown graphs, book graphs, stacked book graphs, and helm graphs, along with kite, cricket, and moth graphs. In particular, we explore various design strategies for these graph families in two sets of laboratory constraints

Mastery-Based Testing in Undergraduate Mathematics

Mastery-based testing is an assessment scheme that challenges students to provide complete solutions to problems derived from clear course concepts. Students are allowed multiple attempts to demonstrate mastery, which helps create a classroom environment where students value persistence toward thorough understanding. In this paper, we describe in detail the benefits and implementation of mastery-based testing in college mathematics courses. We also summarize student response data that show positive reactions to this testing method