Mathematical biology modules based on modern molecular biology and modern discrete mathematics

LacOp: A free web-based lac operon simulation that enhances student learning of gene regulation concepts

Here, we describe a free, web-based simulation of the lac operon, "LacOp," that is designed to enhance the learning of prokaryotic gene regulation and pathways in advanced high school and undergraduate genetics courses. This new electronic resource was created by a team of students in an advanced undergraduate course and is hosted online (http://flask-env.rnwhymamqf.us-west-2.elasticbeanstalk.com/lacop). LacOp has a simple web interface compatible with a range of devices, including smartphones. To determine whether the LacOp simulation enhances student learning from traditional instruction, we introduced the lac operon to undergraduate genetics students through a traditional classroom experience followed by use of the LacOp simulation. Students worked on their own using the included tutorial to create and test the effect of various genotypes on E. coli lactose metabolism and regulation. Upon completion of the tutorial, students showed measurable gains in conceptual understanding of the lac operon. These students also reported a generally favorable opinion of the LacOP simulation as a use of their instructional time.

Fractional stochastic modeling: New approach to capture more heterogeneity

To further capture holding complexities of nature that arise in many fields of science, technology, and engineering, we suggested in this paper a novel approach of modeling. The novel approach is a coupling of fractional differential and integral operators with the stochastic approach. The approach is texted using systems of chaotic problems. The numerical simulation impulsively shows that the new approach is able to capture hiding behaviors that could not be captured by fractional differential and integral operators and the stochastic approach only. We believe that this approach is the future way to model complex problems.

The Math-Biology Values Instrument: Development of a Tool to Measure Life Science Majors' Task Values of Using Math in the Context of Biology

In response to calls to improve the quantitative training of undergraduate biology students, there have been increased efforts to better integrate math into biology curricula. One challenge of such efforts is negative student attitudes toward math, which are thought to be particularly prevalent among biology students. According to theory, students' personal values toward using math in a biological context will influence their achievement and behavioral outcomes, but a validated instrument is needed to determine this empirically. We developed the Math-Biology Values Instrument (MBVI), an 11-item college-level self--report instrument grounded in expectancy-value theory, to measure life science students' interest in using math to understand biology, the perceived usefulness of math to their life science career, and the cost of using math in biology courses. We used a process that integrates multiple forms of validity evidence to show that scores from the MBVI can be used as a valid measure of a student's value of math in the context of biology. The MBVI can be used by instructors and researchers to help identify instructional strategies that influence math-biology values and understand how math-biology values are related to students' achievement and decisions to pursue more advanced quantitative-based courses.

Integrating quantitative thinking into an introductory biology course improves students' mathematical reasoning in biological contexts

Recent calls for improving undergraduate biology education have emphasized the importance of students learning to apply quantitative skills to biological problems. Motivated by students' apparent inability to transfer their existing quantitative skills to biological contexts, we designed and taught an introductory molecular and cell biology course in which we integrated application of prerequisite mathematical skills with biology content and reasoning throughout all aspects of the course. In this paper, we describe the principles of our course design and present illustrative examples of course materials integrating mathematics and biology. We also designed an outcome assessment made up of items testing students' understanding of biology concepts and their ability to apply mathematical skills in biological contexts and administered it as a pre/postcourse test to students in the experimental section and other sections of the same course. Precourse results confirmed students' inability to spontaneously transfer their prerequisite mathematics skills to biological problems. Pre/postcourse outcome assessment comparisons showed that, compared with students in other sections, students in the experimental section made greater gains on integrated math/biology items. They also made comparable gains on biology items, indicating that integrating quantitative skills into an introductory biology course does not have a deleterious effect on students' biology learning.

Teaching biology through statistics: application of statistical methods in genetics and zoology courses

Incorporation of mathematics into biology curricula is critical to underscore for undergraduate students the relevance of mathematics to most fields of biology and the usefulness of developing quantitative process skills demanded in modern biology. At our institution, we have made significant changes to better integrate mathematics into the undergraduate biology curriculum. The curricular revision included changes in the suggested course sequence, addition of statistics and precalculus as prerequisites to core science courses, and incorporating interdisciplinary (math-biology) learning activities in genetics and zoology courses. In this article, we describe the activities developed for these two courses and the assessment tools used to measure the learning that took place with respect to biology and statistics. We distinguished the effectiveness of these learning opportunities in helping students improve their understanding of the math and statistical concepts addressed and, more importantly, their ability to apply them to solve a biological problem. We also identified areas that need emphasis in both biology and mathematics courses. In light of our observations, we recommend best practices that biology and mathematics academic departments can implement to train undergraduates for the demands of modern biology.