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Students begin by generating a coin-flip-based data set that models dye molecule movement across a permeable gel interface. Results are then collapsed into a single predictive data set, which guides a wet-lab measurement of real dye diffusion over time. Experimental and predicted trends show good agreement, enabling discussion of model strengths, limitations, and related misconceptions.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/an-introduction-to-biological-modeling-using-coin-flips-to-predict-the-outcome-of-a-diffusion-activity-lab/594635/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/an-introduction-to-biological-modeling-using-coin-flips-to-predict-the-outcome-of-a-diffusion-activity-lab/594635.png","ImageObject",300,407,{"name":92,"@type":93},"Ben ","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-23","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":8},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the main goal of the diffusion lab activity?","Question",{"text":112,"@type":113},"To improve students’ awareness and comfort with mathematical modeling of biological processes and to deepen their conceptual understanding of diffusion.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How is the simulation data set generated in the activity?",{"text":117,"@type":113},"Students create trajectories using coin flips, where each toss represents a random displacement a dye molecule may undergo in a gelatinous medium.",{"name":119,"@type":110,"acceptedAnswer":120},"How do students connect simulation results to experimental outcomes?",{"text":121,"@type":113},"The class-collapsed simulation is used to predict diffusion over time, and students then measure actual dye diffusion in a wet-lab across a water/gelatin interface for comparison.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},594635,1792775044,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":24,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":144},2336478951081,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","ARTICLES  \nAn Introduction to Biological Modeling Using Coin Flips to Predict the  \nOutcome of a Diffusion Activity  \nGreg Q. Butcher1*, Juan Rodriguez2, Scott Chirhart3, and Troy C. Messina4  \n1 Department of Neuroscience, Thiel College, 75 College Ave., Greenville, PA, 16125  \n2 Department of Basic Sciences, St. Louis College of Pharmacy, 4588 Parkview Place, St. Louis, MO 63110  \n3 Department of Biology, Centenary College of Louisiana, 2911 Centenary Blvd., Shreveport, LA, 71104  \n4 Department of Physics, Berea College, 101 Chestnut St., Berea, KY 40404  \n*Corresponding Author: [gbutcher@thiel.edu](gbutcher@thiel.edu)  \nAbstract: In order to increase students’ awareness for and comfort with mathematical modeling of biological processes, and increase their understanding of diffusion, the following lab was developed for use in 100-level, majors/non-majors biology and neuroscience courses. The activity begins with generation of a data set that uses coin-flips to replicate movement of dye molecules at an interface of a permeable gel. The class results are then collapsed into a single data set that is used to predict the movement of real dye molecules over time, which are then measured by students in a “wet-lab” activity.  \nKeywords: diffusion, predictive, modeling, interdisciplinary  \nINTRODUCTION  \nIn 2011, The American Association for the Advancement of Science (AAAS) released a document entitled Vision and Change in Undergraduate Biology Education: A Call to Action. This document provides a blueprint for reforming biology education that outlines key concepts and skills that prepare biology students for 21st century biology. One recommendation is that students develop skills in modeling and simulations for biological discovery. Here we describe a laboratory activity that provides this experience while elucidating a concept difficult to grasp: diffusion.  \nAll molecules and microscopic particles in suspension undergo diffusion. This phenomenon is driven by constant collisions with surrounding molecules, which causes them to undergo random and unpredictable changes in motion. How such motion is connected to another aspect of diffusion, where bodies move predictably towards regions of lower concentrations, is a concept difficult to get across in a biology curriculum, as has been documented by Meir et al. (2005) and Fisher et al.(2011) .  \nThe following activity was developed to increase students’ awareness for and comfort with modeling of biological processes, and increase their conceptual understanding of diffusion. The activity has been tested in 100-level, majors/non-majors biology and neuroscience courses and a 100-level non-majors physics course. Our approach was to build on the pedagogical principle that active learning more deeply involves students in their own learning of  \nphysical processes (Meltzer and Thornton, 2012) . To that end we had our students learn how random motion drives diffusion by (1) being actively involved in generating trajectories of several molecules undergoing random motion and (2) by analyzing those trajectories and relating them to motion towards regions of lower concentrations. Here the random motion that molecules undergo is simulated with coin tosses, each representing a random displacement that a dye molecule may undergo in a gelatinous medium. Students then complete a “wet-lab” in which they measure actual diffusion of food coloring into gelatin, across a water/gelatin interface, and compare the experimental results to the simulated data set. Good agreement was obtained between the actual experimental and predicted data sets. While students’ predictions may deviate somewhat from the observable diffusion, these discrepancies allow for fruitful class discussions about the strengths and weaknesses of mathematical models and fundamental properties of diffusion. Finally, we assessed students’ improved understanding of diffusion in all of our classes using a questionnaire that was administered bef","cbCaifrOsZfk5Hhr","https://ap.wps.com/l/cbCaifrOsZfk5Hhr","pdf",443374,"English","# Abstract\n# Introduction\n# Materials and Methods\n## Participating institutions and courses\n## Pre-laboratory activities\n## Classroom discussion\n## Homework assignment in experimental classes","[{\"question\":\"What is the main goal of the diffusion lab activity?\",\"answer\":\"To improve students’ awareness and comfort with mathematical modeling of biological processes and to deepen their conceptual understanding of diffusion.\"},{\"question\":\"How is the simulation data set generated in the activity?\",\"answer\":\"Students create trajectories using coin flips, where each toss represents a random displacement a dye molecule may undergo in a gelatinous medium.\"},{\"question\":\"How do students connect simulation results to experimental outcomes?\",\"answer\":\"The class-collapsed simulation is used to predict diffusion over time, and students then measure actual dye diffusion in a wet-lab across a water/gelatin interface for comparison.\"}]","An Introduction to Biological Modeling Using Coin Flips to Predict the Outcome of a Diffusion Activity - Lab | PDF",1792079533,13]