HERE'S YOUR CHANCE

University Modeling Instruction (UMI) is an approach to curriculum and pedagogy that focuses instruction on engaging students in building, validating, and deploying scientific models. Modeling Instruction has been successfully implemented in both high school and university physics courses. Studies within the physics education research (PER) community have identified UMI's positive impacts on learning gains, equity, attitudinal shifts, and self-efficacy. While the success of this pedagogical approach has been recognized within the physics community, the use of models and modeling practices is still being developed for biology. Drawing from the existing research on UMI in physics, we describe the theoretical foundations of UMI and how UMI can be adapted to include an emphasis on models and modeling for undergraduate introductory biology courses. In particular, we discuss our ongoing work to develop a framework for the first semester of a two-semester introductory biology course sequence by identifying the essential basic models for an introductory biology course sequence.

Recent reform efforts in undergraduate biology have recommended transforming course exams to test at more cognitively challenging levels, which may mean including more cognitively challenging and more constructed-response questions on assessments. However, changing the characteristics of exams could result in bias against historically underserved groups. In this study, we examined whether and to what extent the characteristics of instructor-generated tests impact the exam performance of male and female and middle/high- and low-socioeconomic status (SES) students enrolled in introductory biology courses. We collected exam scores for 4810 students from 87 unique exams taken across 3 yr of the introductory biology series at a large research university. We determined the median Bloom's level and the percentage of constructed-response questions for each exam. Despite controlling for prior academic ability in our models, we found that males and middle/high-SES students were disproportionately favored as the Bloom's level of exams increased. Additionally, middle/high-SES students were favored as the proportion of constructed-response questions on exams increased. Given that we controlled for prior academic ability, our findings do not likely reflect differences in academic ability level. We discuss possible explanations for our findings and how they might impact how we assess our students.

This study demonstrates a small, but significant, difference in prior understanding of basic biological concepts between students enrolled in majors' versus nonmajors' introductory biology courses. By the end of their respective courses, nonmajors demonstrated greater improvement in posttest scores than did majors. Furthermore, although initially students in the major course had a significantly more positive attitude towards science, especially in terms of personal comfort with science, by the end of the course this difference disappears. Following a semester of instruction, the attitudes of nonmajors generally improved, but student attitudes in the majors' classes declined in nearly all categories. We demonstrate a significant instructor effect in these results.

Course-based undergraduate research experiences (CUREs) have grown in popularity, particularly within introductory biology courses, to provide more students with authentic research experiences. CUREs have been shown to have many of the same positive effects as conventional research experiences; however, most assessments of CUREs lack an appropriate comparison group to evaluate their effectiveness. Here, we introduced a CURE into an introductory biology lab at a regional public university but maintained a traditional, "cookie-cutter" lab in half the lab sections over a 3-year period. We compared changes in test scores and survey responses, final lab and lecture scores, and D, F, withdrawal, and incomplete (DFWI) and retention rates between non-honors biology students in each group. While both groups showed significant improvement in test scores, only transfer students had significantly greater improvement in the CURE vs traditional lab. Students in both groups showed significant increases in self-confidence in some lab-related tasks, but differences in these changes were generally not significant between groups. There were no significant differences in final lecture score, lab score, DFWI rate, or retention rate. Factors affecting the lack of measured CURE success may include the type of CURE chosen, student career interests, and COVID-19; other positive impacts of the CURE may not have been captured by our measurements. This study demonstrates the importance of carefully choosing a CURE to match the student population, as well as assessing the CURE's impact against a comparison group.

Previous article Next article On the Extension of the Class of Stable DistributionsV. M. KruglovV. M. Kruglovhttps://doi.org/10.1137/1117081PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] B. V. Gnedenko and , A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Cambridge, Mass., 1962 Google Scholar[2] Yu. V. Linnik, Decomposition of probability distributions, Edited by S. J. Taylor, Dover Publications Inc., New York, 1964xii+242 MR0189085 (32:6512) 0121.35502 Google Scholar[3] B. V. Gnedenko, Some theorems on distribution functions, Učenie Zapiski Moskovskogo Univ., 30 (1939), 61–82, (In Russian.) Google Scholar[4] V. M. Kruglov, A note on infinitely divisible distributions, Theory Prob. Applications, 15 (1970), 319–324 10.1137/1115038 0329.60011 LinkGoogle Scholar[5] I. A. Ibragimov and , Yu. V. Linnik, Independent and stationary sequences of random variables, Wolters-Noordhoff Publishing, Groningen, 1971, 443– MR0322926 (48:1287) 0219.60027 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Functional L.I.L. for the Upper Extremes of i.i.d. Random Variarbles from a Sub-class of Heavy Tailed Distributions31 October 2021 | Journal of the Indian Society for Probability and Statistics, Vol. 22, No. 2 Cross Ref Functional law of the iterated logarithm for partial sum processes of non-negative valued iid random variables belonging to the domain of partial attraction of a semi-stable lawStatistics & Probability Letters, Vol. 137 Cross Ref A Log Log Law for Subsequences of Delayed Random Sums27 July 2017 | Journal of the Indian Society for Probability and Statistics, Vol. 18, No. 2 Cross Ref Merging to Semistable ProcessesI. 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Megyesi25 July 2006 | Theory of Probability & Its Applications, Vol. 47, No. 1AbstractPDF (220 KB)On Lévy–Fréchet processes and related self-similar and semi-self-similar onesChaos, Solitons & Fractals, Vol. 14, No. 5 Cross Ref ON LÉVY STABLE AND SEMISTABLE DISTRIBUTIONS20 November 2011 | Fractals, Vol. 09, No. 03 Cross Ref Rarely Observed Sample MaximaL. Canto E Castro, L De Haan, and M. G. Temido25 July 2006 | Theory of Probability & Its Applications, Vol. 45, No. 4AbstractPDF (90 KB)A law of the iterated logarithm for semistable laws on vector spaces and homogeneous groupsJournal of Mathematical Sciences, Vol. 89, No. 5 Cross Ref Characterization of multivariate distributions through a functional equation of their characteristic functionsJournal of Statistical Planning and Inference, Vol. 63, No. 2 Cross Ref Series representation for semistable laws and their domains of semistable attractionJournal of Theoretical Probability, Vol. 9, No. 4 Cross Ref The Domains of Attraction of Semistable LawsI. V. Grinevich and Yu. S. Khokhlov12 July 2006 | Theory of Probability & Its Applications, Vol. 40, No. 2AbstractPDF (670 KB)Moments of measures attracted to operator semi-stable lawsStatistics & Probability Letters, Vol. 24, No. 3 Cross Ref Recurrence and transience of operator semi-stable processesProceedings of the Japan Academy, Series A, Mathematical Sciences, Vol. 71, No. 5 Cross Ref XVI Seminar on Stability Problems of Stochastic Models17 July 2006 | Theory of Probability & Its Applications, Vol. 37, No. 4AbstractPDF (5240 KB)A characterization of gamma mixtures of stable laws motivated by limit theoremsStatistica Neerlandica, Vol. 46, No. 2-3 Cross Ref ON CHARACTERIZATIONS THROUGH MIXED SUMS28 June 2008 | Australian Journal of Statistics, Vol. 34, No. 2 Cross Ref The Suzdal International Seminar of 1991 on Stability Problems for Stochastic Models17 July 2006 | Theory of Probability & Its Applications, Vol. 36, No. 4AbstractPDF (5581 KB)Law of iterated logarithm for random subsequencesStatistics & Probability Letters, Vol. 12, No. 3 Cross Ref Limit theorems for probability measures on simply connected nilpotent lie groupsJournal of Theoretical Probability, Vol. 4, No. 2 Cross Ref On a Scheme of Partial SummationE. 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A large body of evidence suggests that an approximate number sense allows humans to estimate numerosity in sensory scenes. This ability is widely observed in humans, including those without formal mathematical training. Despite this, many outstanding questions remain about the nature of the numerosity representation in the brain. Specifically, it is not known whether approximate numbers are represented as scalar estimates of numerosity or, alternatively, as probability distributions over numerosity. In the present study, we used a multisensory decision task to distinguish these possibilities. We trained human subjects to decide whether a test stimulus had a larger or smaller numerosity compared with a fixed reference. Depending on the trial, the numerosity was presented as either a sequence of visual flashes or a sequence of auditory tones, or both. To test for a probabilistic representation, we varied the reliability of the stimulus by adding noise to the visual stimuli. In accordance with a probabilistic representation, we observed a significant improvement in multisensory compared with unisensory trials. Furthermore, a trial-by-trial analysis revealed that although individual subjects showed strategic differences in how they leveraged auditory and visual information, all subjects exploited the reliability of unisensory cues. An alternative, nonprobabilistic model, in which subjects combined cues without regard for reliability, was not able to account for these trial-by-trial choices. These findings provide evidence that the brain relies on a probabilistic representation for numerosity decisions.

Random walk is a randomly walk process that describes the path including a succession of random steps in the mathematical region. A procedure for estimating the likely position of a point exposed to random motions in probability theory, given the probabilities (which remain constant at each step) of traveling a certain distance in a certain direction. A Markov process that exhibits future behavior independent of prior history is the random walk. This paper will discover the classic recurrence Theorem concerning random walks on the d-dimensional integer lattice, and demonstrate the leads to complete generality with simple methods supported by String’s Approximation. Furthermore, this essay will explore the situation that walker randomly walks in different dimensions and discover that random walk on dimensions one and two will return to the initial point, dimension three and higher dimensions will not. The meaning of this essay is to help more people have some basic understanding with random walk and to know there are some applications of random walk.

Muth’s Rational Expectations Hypothesis, That “…The Subjective Probability Distributions Are Distributed Around an Objective Probability Distribution, for a given Information Set…” is an Oxymoron. It Can Be Corrected by Amending It to Read “…The Subjective Probability Distributions Are Distributed Around a Subjective Consensus Probability Distribution, for a given Information Set…”

Biology education researchers seek to improve biology education, particularly at the introductory level, yet there is little documentation about what is actually happening in introductory biology. To characterize the landscape of learning expectations for introductory biology, we analyzed course-level learning objectives (n = 1108) and course schedules from 188 nonmajor, mixed major, and major introductory biology syllabi. We analyzed syllabi collected from a diverse range of U.S. institution types to uncover insights about instructional design decisions for introductory biology. Our analysis revealed two distinct nonmajor course types: content and issues-based courses. We found syllabi tend to focus on low-cognitive skills and factual content that is essentially a march in step with a typical textbook table of contents, rarely including core competencies or socioscientific issues (SSIs) other than in nonscience major issues-based courses. Our work contributes more evidence that faculty struggle to write course-level learning objectives. Our findings suggest that there is much work to do if Vision and Change are to become more than simply a vision–to be actualized as change–including developing CLOs for introductory biology as a first step toward creating actionable instructional change.

BackgroundUnderstanding evolution is an important part of undergraduate biology education. Despite its importance, however, students often struggle to understand evolution, often holding preconceived notions of what evolution is. Here, we investigate how students in both majors and non-majors introductory biology define and conceive of evolution at the start of the semester for a two-year college and a four-year university near each other. We analyze open-ended responses to an in-class activity on the first day of the semester that asked students to define evolution, generating insight into how students are thinking of evolution prior to any formal instruction on evolution in college.ResultsOur analysis of over 300 student responses reveals that students hold diverse conceptions about evolution, with some students perceiving evolution in the context of evolutionary processes while other students define evolution by referring to perceived evolutionary consequences. In addition, we identify multiple non-normative conceptions about evolution, including students viewing evolution and natural selection as synonymous and not recognizing other evolutionary forces, and find that very few students likely have developed mental models linking evolution and genetics. In addition, we find few differences between how students at the two- and four-year institutions perceive evolution, and similarly few differences between students in a majors and non-majors introductory biology, suggesting that these conceptions of evolution are widespread at the beginning of introductory biology, regardless of major or institution.ConclusionsWe situate our results in the existing literature examining student conceptions of evolution, with our results extending past work that has primarily relied on more closed-ended questions or focused on specific evolutionary concepts (e.g., natural selection). Our results largely align with past work on student thinking of evolution but provide a broader, more holistic perspective at the ideas and framework that students are drawing upon when introductory biology instructors first introduce the term ‘evolution’. We conclude our paper by discussing implications for the biology education research community as well as instructors.

Understanding the relationship between the structure and function of biological molecules (carbohydrates, lipids, proteins, and nucleic acids) is a fundamental concept covered in an undergraduate introductory biology course with which students often struggle. Students at this level often feel intimidated when asked to recall and differentiate between the specifics of each macromolecule including monomers, polymers, types of bonds or functional groups present, and the function of each. Demonstrating a deeper understanding of the material such as the relationship between structure and function is even more challenging since this requires higher-level conceptualization and synthesis skills. While lecturing can deliver an abundance of facts, providing students with hands-on opportunities to discover information themselves and practice putting together complex ideas often results in an increase in engagement and ultimately student satisfaction and confidence in the sciences. We developed a student-designed 3D modeling project in order to provide our students a hands-on approach to learning about biological macromolecules. The project begins with several low-stakes active learning activities and culminates with model design and peer teaching of an assigned macromolecule. Our observations and evaluations collected over the past twelve semesters of implementation in a small introductory biology course for science majors suggest that students who fully participate in this project show an increase in their perceived understanding of this material and engagement in the course. In this lesson we provide a detailed description of our activity including supporting materials and suggested adaptations for online or large classrooms. <em>Primary Image:</em>&nbsp;3D printed phospholipids. Individual phospholipids were 3D printed and colored using permanent marker. Magnets were added after printing to represent intermolecular forces that allow phospholipid head groups to interact within the phospholipid bilayer of cells. Image credit: Emily M. Nowicki, picture taken in-house.

Students enter college exceedingly confident that they will earn high grades and engage themselves fully in their courses (e.g., attend all of their classes and help-sessions, submit extra-credit work). However, students' grades and academic behaviors often do not match their expectations (Jensen & Moore, 2008; Moore, 2006b; Moore & Jensen, 2007a). This is especially true in introductory science courses, where grades and academic engagement are often low, even in courses taught by award-winning instructors (Congas et al., 1997; Friedman et al., 2001). Students' poor academic behaviors (e.g., skipping class, ignoring opportunities to improve their grades) often bewilder instructors, who understand that academic success depends largely on students' levels of academic engagement. In this study, we tried to understand what underlies students' academic behaviors and overconfidence. To do this, we analyzed the grades, academic behaviors, and academic predictions of students who earned differing final grades in a large introductory biology course. We asked three sets of questions, the first of which involved grades earned by students on exams throughout the course. How, on average, do students' grades fluctuate throughout the semester? Do students predict high grades late into the semester because their grades are high until late into the semester? The second set of questions involved students' beliefs about the academic behaviors that are important for success, such as class attendance, submission of extra-credit assignments, and attendance at help-sessions (Moore, 2006b; Moore & Jensen, 2007b). Students know that these behaviors are important for their academic success (Jensen & Moore, in press; Moore, 2003, 2006a). However, do students who earn different final grades actually exhibit different academic behaviors? Finally, we wondered how students' scores on exams throughout the semester affect students' confidence about their final grades. How accurately do students predict their grades throughout the semester? That is, how is students' confidence about their final grades affected by feedback (i.e., their grades on exams) that they receive during the semester? Methods Site of the Study & Its Students This study included 278 students enrolled in an introductory mixed-majors biology course at the University of Minnesota. The course covered topics typical of an introductory biology course, including evolution, cellular structure and function, molecular biology, genetics, and ecology. The population was 51% male and 49% female, averaged a 19.8 on the ACT, had a mean age of 19 years, and on average ranked in the 57th percentile of their high school classes. All students were taught in the same classroom by the same instructor who used identical syllabi, textbooks, grading rubrics, and pedagogical approaches. Grade Groups, Grade Cut-Offs & Determinations of Final Grades Students were grouped according to their final grades in the course, which were determined as follows: A= 90% and above, B= 80-89%, C= 70-79%, D= 60-69%, F= 59% and below. Course grades were calculated by averaging two equal scores: the exam score and the lab/homework score. The exam score (50%) included each of the three equally-weighted midterm exams (10% each) and a cumulative final exam (20%). The lab/homework score (50%) included the grade earned in the laboratory portion of the course (30%) and the homework component of the grade (20%), which was based on the completion of 15 assignments (some of which were done in class) throughout the semester. Class attendance was recorded every day with the submission of short, in-class writing assignments. Help Sessions An optional help-session was offered before each exam. These sessions were administered by a teaching assistant who had no knowledge of, or input to, the upcoming exams (i.e., students who attended the help-sessions got no inside information about that exam). …

Undergraduate biology students describe fear of negative evaluation (FNE), defined as a sense of dread associated with being unfavorably evaluated in a social situation, as negatively affecting their experiences in active learning courses. Yet, few studies have examined who is prone to experiencing FNE, the severity and duration of FNE, and whether the effects of FNE are experienced equally among undergraduates. To address these gaps, we surveyed 494 undergraduates enrolled in active learning introductory biology courses about their FNE as it relates to students in their courses (classmate FNE) and to their instructor (instructor FNE). Students reported higher instructor FNE than classmate FNE. Using linear regressions, we found that women and nonbinary students, persons excluded based on ethnicity or race (PEERs), continuing-generation college students, LGBTQ+ students, and non-native English speakers had higher instructor FNE than their respective counterparts. PEER students also had higher classmate FNE than white students. Women, nonbinary, and PEER students were more likely than men and white students to report a greater negative impact of FNE on their abilities to articulate their thoughts about science in class. This work highlights the importance of reducing FNE with the intent to create more equitable active learning biology classrooms.

STEM education reform stresses the importance of a comprehensive understanding of science fundamentals and the development of science and engineering practices. As such, many engineering students must complete a core set of courses, including biology; however, this course is often designed for life sciences majors. One solution to this mismatch is to create an introductory biology course targeted to non‐biology STEM majors that introduces students to biology through a computational lens. Avida‐ED is a digital evolution software platform in which populations of digital organisms undergo actual—not simulated—evolutionary change, making evolution come alive through its observation in action. Integrating Avida‐ED provides a unique and novel approach to engaging engineering students in biological concepts within a computational environment, allowing them to exercise science and engineering practices in an authentic research experience. The design of this one‐semester course, “Integrative Biology: From DNA to Populations,” including its incorporation of a digital evolution lab, creates a way for computational science and engineering students to engage with biology within a context that is familiar and interesting.

In mathematics and statistics, the desire to eliminate mathematical tedium and facilitate exploration has lead to computer algebra systems. These computer algebra systems allow students and researchers to perform more of their work at a conceptual level. The design of generic algorithms for tedious computations allows modelers to push current modeling boundaries outward more quickly. Probability theory, with its many theorems and symbolic manipulations of random variables is a discipline in which automation of certain processes is highly practical, functional, and efficient. There are many existing statistical software packages, such as SPSS, SAS, and S-Plus, that have numeric tools for statistical applications. There is a potential for a probability package analogous to these statistical packages for manipulation of random variables. The software package being developed as part of this dissertation, referred to as “A Probability Programming Language” (APPL) is a random variable manipulator and is proposed to fill a technology gap that exists in probability theory. My research involves developing algorithms for the manipulation of discrete random variables. By defining data structures for random variables and writing algorithms for implementing common operations, more interesting and mathematically intractable probability problems can be solved, including those not attempted in undergraduate statistics courses because they were deemed too mechanically arduous. Algorithms for calculating the probability density function of order statistics, transformations, convolutions, products, and minimums/maximums of independent discrete random variables are included in this dissertation.