[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-585951-105":59,"doc-detail-585951-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","examining-opportuites-to-learn-definite-integrals-in-widely-used-calculus-textbooks","EXAMINING OPPORTUITES TO LEARN DEFINITE INTEGRALS IN WIDELY USED CALCULUS TEXTBOOKS","","The study investigates learning opportunities for definite integrals in three widely used U.S. calculus textbooks. Definitions, worked examples, and exercise problems are coded using research-based cognitive resources for definite integrals. Results indicate limited opportunities for students to explore multiplicative relationships between two quantities and to understand definite integrals through the idea of adding small pieces. The work is framed around how textbooks present knowledge units and accumulating-up pieces representations.",{"@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":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/examining-opportuites-to-learn-definite-integrals-in-widely-used-calculus-textbooks/585951/",{"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/examining-opportuites-to-learn-definite-integrals-in-widely-used-calculus-textbooks/585951.png","ImageObject",300,407,{"name":92,"@type":93},"Jordan Avery","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-06","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":81},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the main focus of the study?","Question",{"text":112,"@type":113},"The study examines how widely used calculus textbooks provide learning opportunities for understanding definite integrals, based on coded definitions, examples, and exercises.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are the textbook materials analyzed?",{"text":117,"@type":113},"Definitions, worked examples, and exercise problems are coded using research-based cognitive resources related to definite integrals.",{"name":119,"@type":110,"acceptedAnswer":120},"What do the results suggest about students’ learning opportunities?",{"text":121,"@type":113},"The results indicate limited opportunities for students to explore multiplicative relationships between quantities and to use “adding small pieces” to build understanding of definite integrals.","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},585951,1792056423,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":81,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":44,"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":129,"read_time":143,"preview_page_count":4},1099523882367,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","EXAMINING OPPORTUITES TO LEARN DEFINITE INTEGRALS IN WIDELY  \nUSED CALCULUS TEXTBOOKS  \nDae S. Hong  \nUniversity of Iowa  \n[dae-hong@uiowa.edu](dae-hong@uiowa.edu)  \nThis study explores opportunities to learn definite integrals in three widely used textbooks in the U.S. Definitions, worked examples, and exercise problems were coded using research – based cognitive resources in definite integrals. The results show that limited opportunities for students to explore multiplicative relationship between two quantities and adding small pieces to understand definite integrals.  \nKeywords: cognitive resources, integral, learning opportunities, textbooks  \nIntroduction  \nIn the United States, Calculus 1 is a core and beginning course for students heading into the disciplines of science, technology, engineering, and mathematics (STEM). Many experts in teaching calculus view an understanding of the integral as a necessary central concept or skill for genuine understanding of first-year calculus (Jones, 2013; Sofronas et al., 2011) . While understanding of the integral is necessary, several existing studies demonstrate students’challenges as well as types of knowledge needed to understand the integral concept (Jones, 2013; Mahir, 2009; Sealey, 2014), illustrating that, in many cases, students are able to correctly integrate functions but do not know how to interpret it in context and tend not to use types of knowledge needed to understand integral conceptually. In this study, we examined how widely used calculus textbooks provide learning opportunities to students. These are our research questions that we attempted to answer.  \n• What units of knowledge about definite integral do widely used calculus textbooks provide to students?  \n• How do widely used calculus textbooks provide opportunities for students to be familiar with adding up pieces symbolic form to introduce the concepts of integral?  \nRelated literature  \nHow students learn integral concepts  \nAccording to experts in teaching calculus, there are three significant interpretations of definite integrals: 1) the integral as net change or accumulated total change, 2) the integral as area, and 3) techniques of integration (Ely, 2017; Sofronas et al., 2011) . Previous studies show that students are able to procedurally calculate integrals but are not able to explain what they are doing and are not able to define the definite integral (Rasslan & Tall, 2002) . What we can learn from these studies is students are very familiar with certain interpretations ofthe integral (area under a curve, anti – derivative, or techniques of integration), but it is challenging for them to understand why the definite integral represents area under a curve or in other contexts such as physics and engineering (Ely, 2017; Jones, 2015; Sealey, 2014) . More recently, in addition to pointing out students’ familiarity to certain interpretations of integrals, researchers have explored questions about types of knowledge students need and coordinate to expand their understanding  \nLamberg, T., & Moss, D. (2023). Proceedings of the forty-fifth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2). University of Nevada, Reno.  \n853  \nArticles published in the Proceedings are copyrighted by the authors.  \nof definite integral (Larsen, Marrongelle, Bressoud, & Graham, 2016) . This idea led to examination of small units of ideas that students need to activate to expand their understanding of definite integral (Jones, 2013) because it might be too simplistic to say that understanding mathematical topics requires a single idea (Harlow & Bianchini, 2020) . With examination of small units of ideas, in addition to think about area under a curve, and anti – derivative, we can look at more fine-grained element of knowledge students need to coordinate to expand meaning of definite integrals. Sealey (2014) described four different layers − limit, summation,","cbCaiaDET5Rmg4QD","https://ap.wps.com/l/cbCaiaDET5Rmg4QD","pdf",257271,"English","# Introduction\n# Related literature\n## How students learn integral concepts\n## Exploring calculus students’ learning opportunities","[{\"question\":\"What is the main focus of the study?\",\"answer\":\"The study examines how widely used calculus textbooks provide learning opportunities for understanding definite integrals, based on coded definitions, examples, and exercises.\"},{\"question\":\"How are the textbook materials analyzed?\",\"answer\":\"Definitions, worked examples, and exercise problems are coded using research-based cognitive resources related to definite integrals.\"},{\"question\":\"What do the results suggest about students’ learning opportunities?\",\"answer\":\"The results indicate limited opportunities for students to explore multiplicative relationships between quantities and to use “adding small pieces” to build understanding of definite integrals.\"}]","EXAMINING OPPORTUITES TO LEARN DEFINITE INTEGRALS IN WIDELY USED CALCULUS TEXTBOOKS | PDF",23]